Apparatus and method for diagnosing osteoporosis

ABSTRACT

The apparatus for diagnosing osteoporosis in the present invention radiates repeated ultrasonic pulses Ai toward cortical bone Mb in a subject and receives echoes Ae from the bone Mb. The received signal is converted to a digital echo signal by an A/D converter 8, and the echo level is detected by a CPU 11. The CPU 11 extracts the maximum echo level from the echo levels detected during the measurement period and calculates the acoustic impedance Zb of the cortical bone based on the maximum echo level which has been extracted. The bone density of the subject is calculated from the detected acoustic impedance Zb of the cortical bone using a predetermined recurrence formula. The acoustic impedance of bone is given by the square root of  the elastic modulus×density! of bone, and since the elastic modulus of bone increases (or decreases) as bone density increases (or decreases), the elastic modulus of bone and bone density play a synergistic role in the acoustic impedance. The acoustic impedance Zb of bone is thus a good index for assessing bone density.

DESCRIPTION

1. TECHNICAL FIELD

This invention relates to an ultrasonic reflection type of apparatus andmethod for diagnosing osteoporosis by emitting ultrasonic pulses towardpredetermined cortical bone in a subject so as to measure the echolevels from the surface of the cortical bone.

2. BACKGROUND ART

With the advent of an ageing society in recent years, the bone diseasereferred to as osteoporosis has become a problem. This is a disease inwhich the loss of bone calcium results in brittleness and susceptibilityto fractures with minimal trauma, and can cause the elderly to becomebedridden. The physical diagnosis of osteoporosis is managed by theprecise measurement of bone density using a diagnostic apparatusfeaturing the use of X-rays such as DXA, but problems involved inphysical diagnosis with X-rays are that the equipment is large andexpensive, and its use is limited in many ways in the interests ofprotecting against harm caused by radiation exposure.

Diagnostic apparatuses featuring the use of transmitted ultrasonic wavesor reflected ultrasonic waves have begun to enjoy more popularity assimple devices which do not suffer from such drawbacks.

The diagnostic apparatuses noted in Japanese Laid-Open PatentApplication 2-104337 and U.S. patent application Ser. No. 193,295 areknown as ultrasonic transmitting types of diagnostic devices. In thesediagnostic apparatuses, the acoustic velocity in bone is measured bysetting up two ultrasonic transducers facing each other on either sideof a part of a subject's body, so that ultrasonic pulses are emittedfrom one ultrasonic transducer at the osseous tissue, and the ultrasonicpulses passing through the osseous tissue are received by the otherultrasonic transducer. The extent of osteoporosis is diagnosed on theassumption that a slower acoustic velocity in osseous tissue indicateslower bone density due to loss of bone calcium.

The theoretical basis linking bone density and acoustic velocity isuncertain, however. Strictly speaking, the acoustic velocity in osseoustissue is not proportional to bone density, but is given by the squareroot of the elastic modulus of bone/bone density!. Furthermore, becausethe elastic modulus of bone and bone density play mutually cancellingroles in acoustic velocity, where increases in the bone density(denominator) are met by increases in the elastic modulus of bone(numerator), the acoustic velocity in osseous tissue is not capable ofsensitive response to increases in bone density. As such, there is notthat high a correlation between the acoustic velocity in osseous tissueand bone density. Reliability is accordingly a problem in conventionalultrasonic transmission types of diagnostic apparatuses in which bonedensity is estimated on the basis of the acoustic velocity in osseoustissue.

Ultrasonic reflection types of diagnostic apparatuses have meanwhilebeen proposed by the applicant in Japanese Patent Applications 6-310445,7-140730, 7-140731, 7-140732, 7-140733, and 7-140734, and InternationalLaid-Open Patent Application WO 96/18342. In these diagnosticapparatuses, a single ultrasonic transducer capable of both transmissionand reception is used to emit ultrasonic pulses toward cortical bone ina subject, echoes reflected on the surface of the cortical bone arereceived, and the acoustic impedance of the subject's cortical bone iscalculated on the basis of the resulting echo data. The progress ofosteoporosis is then diagnosed based on the level of the acousticimpedance thus calculated.

The acoustic impedance of bone is given by the square root of theelastic modulus×density! of bone, and since, as described above, theelastic modulus of bone increases (or decreases) as bone densityincreases (or decreases), the elastic modulus of bone and bone densityplay a synergistic role in acoustic impedance. Thus, the latterultrasonic reflection type of apparatus in which acoustic impedance isused as an index can be considered more reliable because it is capableof more sensitive response to the extent of the progress of osteoporosisthan is the former ultrasonic transmission type of apparatus in whichacoustic velocity is used as an index.

Although acoustic impedance can be considered a sensitive indicator ofthe progress of osteoporosis, in the final analysis it is only an indexof bone density, which does not mean that the bone density itself isdetermined. Furthermore, when the acoustic impedance of cortical bone islower than that of soft tissue, or when the cortical bone is thinnerthan the ultrasonic wavelength, there is a problem in that the acousticimpedance of cortical bone cannot be measured or that such measurementis uncertain.

In view of the foregoing, a first object of the present invention is toprovide an ultrasonic reflection type of apparatus and method fordiagnosing osteoporosis, which is simple, with no danger of exposure toradiation, yet is capable of determining bone density. A second objectof the present invention is to provide an ultrasonic reflection type ofapparatus and method for diagnosing osteoporosis, which is capable ofhighly reliable diagnosis, even when the acoustic impedance of thecortical bone is lower than that of the soft tissue and when thecortical bone is thinner than the ultrasonic wavelength.

SUMMARY OF THE INVENTION

In the apparatus (and method) for diagnosing osteoporosis in the presentinvention, ultrasonic pulses are repeatedly emitted toward cortical bonein a subject, the echoes reflected on the surface of the cortical boneat that time are received, and osteoporosis is diagnosed based on theresulting echo data.

As such, a first aspect of the present invention is to provide anapparatus for diagnosing osteoporosis, comprising: an echo leveldetecting means for detecting the echo level of the echoes reflected onthe surface of the cortical bone when the ultrasonic pulses are emitted;a maximum echo level extracting means for extracting the maximum echolevel from among the echo levels thus detected; a reflection coefficientcalculating means for calculating the ultrasonic reflection coefficientat the interface between the soft tissue and cortical bone of thesubject based on the maximum echo level that has been extracted; and abone density calculating means for calculating the density of thesubject's cortical bone using a predetermined recurrence formula for thecortical bone density relative to the ultrasonic reflection coefficient.

In a preferred embodiment of the bone density calculating means, therecurrence formula for the cortical bone density relative to theultrasonic reflection coefficient is given in the form of Formula (1) or(2)

    ρ=α'R+β'                                    (1)

ρ: density of cortical bone kg/m³ !

R: ultrasonic reflection coefficient at interface between soft tissueand cortical bone of subject

α': regression coefficient kg/m³ !

β': section kg/m³ !

The regression coefficient α' should be established within the range of588 to 1100, and the section β' should be established within the rangeof 953 to 1060.

    ρ=B'R.sup.A'                                           ( 2)

A': regression coefficient

B': constant sec/m!

A second aspect of the present invention is to provide an apparatus,comprising: an echo level detecting means for detecting the echo levelof the echoes reflected on the surface of the cortical bone when theultrasonic pulses are emitted; a maximum echo level extracting means forextracting the maximum echo level from among the echo levels thusdetected; an acoustic impedance calculating means for calculating theacoustic impedance of the subject's cortical bone based on the maximumecho level that has been extracted; and a bone density calculating meansfor calculating the density of the subject's cortical bone using apredetermined recurrence formula for the cortical bone density relativeto the acoustic impedance.

In a preferred embodiment of the bone density calculating means, therecurrence formula for cortical bone density relative to acousticimpedance is given by Formula (3) or (4).

    ρ=αZb+β                                     (3)

ρ: density of cortical bone kg/m³ !

Zb: acoustic impedance of cortical bone in subject kg/m² sec!

α: regression coefficient sec/m!

β: section kg/m³ !

The regression coefficient α should be established within the range of1.27×10⁻⁴ to 2.34×10⁻⁴, and the section β should be established withinthe range of 646 to 887.

    ρ=BZb.sup.A                                            ( 4)

A: regression coefficient

B: constant sec/m!

The regression coefficient A should be established with the range of0.239 to 0.445, and the constant B should be established within therange of 10⁰.239 to 10¹.55.

A third aspect of the present invention is to provide an apparatus fordiagnosing osteoporosis, comprising: an echo waveform detecting meansfor detecting the reception waveform of the echoes reflected on thesurface of the cortical bone when the ultrasonic pulses are emitted; amaximum echo waveform extracting means for extracting the maximum echoreception waveform by comparing the plurality of echo receptionwaveforms that have been detected; a Fourier transform treatment meansfor finding the maximum echo spectrum by the Fourier transform treatmentof the maximum echo reception waveform; and a complex reflectioncoefficient calculating means for calculating the ultrasonic complexreflection coefficient (complex acoustic characteristics data) ofcortical bone relative to the soft tissue of the subject based on themaximum echo spectrum thus determined, wherein osteoporosis is diagnosedon the basis of the ultrasonic complex reflection coefficient thuscalculated.

A preferred embodiment of the third aspect further comprises adiagnostic means for obtaining amplitude data and phase data from theultrasonic complex reflection coefficient thus calculated, and fordiagnosing osteoporosis based on the resulting amplitude and phase data.

A fourth aspect of the present invention is to provide an apparatus fordiagnosing osteoporosis, comprising: an echo waveform detecting meansfor detecting the reception waveform of the echoes reflected on thesurface of the cortical bone when the ultrasonic pulses are emitted; amaximum echo waveform extracting means for extracting the maximum echoreception waveform by comparing the plurality of echo receptionwaveforms that have been detected; a Fourier transform treatment meansfor finding the maximum echo spectrum by the Fourier transform treatmentof the maximum echo reception waveform; and a complex acoustic impedancecalculating means for calculating the complex acoustic impedance(complex acoustic characteristics data) of the subject's cortical bonebased on the maximum echo spectrum thus determined, wherein osteoporosisis diagnosed on the basis of the complex acoustic impedance thuscalculated.

A preferred embodiment of the fourth aspect further comprises adiagnostic means for obtaining amplitude data and phase data from thecomplex acoustic impedance thus calculated, and for diagnosingosteoporosis based on the resulting amplitude and phase data.

A fifth aspect of the present invention is to provide a method fordiagnosing osteoporosis, wherein an ultrasonic transducer is placed on apredetermined area on the surface of a subject's skin, ultrasonic pulsesare repeatedly emitted toward cortical bone below the skin, the echoesreflected on the surface of the cortical bone at that time are receivedso as to detect the echo level, the maximum echo level is extracted fromthe echo levels thus detected, the ultrasonic reflection coefficient atthe interface between the soft tissue and the cortical bone of thesubject is calculated based on said extracted maximum echo level, andthe density of the subject's cortical bone is then calculated using apredetermined recurrence formula for the cortical bone density relativeto the ultrasonic reflection coefficient.

A sixth aspect of the present invention is to provide a method fordiagnosing osteoporosis, wherein an ultrasonic transducer is placed on apredetermined area on the surface of a subject's skin, ultrasonic pulsesare repeatedly emitted toward cortical bone below the skin, the echoesreflected on the surface of the cortical bone at that time are receivedso as to detect the echo level, the maximum echo level is extracted fromthe echo levels thus detected, the acoustic impedance of the corticalbone of the subject is calculated based on said extracted maximum echolevel, and the density of the subject's cortical bone is then calculatedusing a predetermined recurrence formula for the cortical bone densityrelative to the acoustic impedance.

A seventh aspect of the present invention is to provide a method fordiagnosing osteoporosis, wherein an ultrasonic transducer is placed on apredetermined area on the surface of a subject's skin, ultrasonic pulsesare repeatedly emitted toward cortical bone below the skin, thereception waveforms of the echoes reflected on the surface of thecortical bone at that time are received so as to detect the echoreception waveforms, the maximum echo is extracted from the echoreception waveforms thus detected, the maximum echo spectrum isdetermined by the Fourier transform treatment of the maximum echoreception waveform, the ultrasonic complex reflection coefficient of thecortical bone relative to the soft tissue of the subject is calculatedbased on the maximum echo spectrum that has been determined, andosteoporosis is diagnosed based on the amplitude data and phase dataobtained from the ultrasonic complex reflection coefficient thuscalculated.

An eighth aspect of the present invention is to provide a method fordiagnosing osteoporosis, wherein an ultrasonic transducer is placed on apredetermined area on the surface of a subject's skin, ultrasonic pulsesare repeatedly emitted toward cortical bone below the skin, thereception waveforms of the echoes reflected on the surface of thecortical bone at that time are received so as to detect the echoreception waveforms, the maximum echo is extracted from the echoreception waveforms thus detected, the maximum echo spectrum isdetermined by the Fourier transform treatment of the maximum echoreception waveform, the complex acoustic impedance of the cortical boneof the subject is calculated based on the maximum echo spectrum that hasbeen determined, and osteoporosis is diagnosed based on the amplitudedata and phase data obtained from the complex acoustic impedance thuscalculated.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram depicting the electrical structure of theapparatus for diagnosing osteoporosis in a first embodiment of theinvention;

FIG. 2 is a schematic outer view of the same apparatus;

FIGS. 3 through 6 are illustrations used to describe the operation ofthe apparatus;

FIG. 7 is a flow chart of the operation of the same apparatus;

FIG. 8 is a graph of the regression line for cortical bone density ρrelative to the acoustic impedance Zb, and is used to describe thecontents of the bone density calculating subprogram constituting thesame apparatus;

FIG. 9 is a graph of the regression line for cortical bone density ρrelative to the acoustic impedance Zb, and is used to describe thecontents of the bone density calculating subprogram in a fourthembodiment;

FIG. 10 is a graph of the regression line for cortical bone density ρrelative to the acoustic impedance Zb, and is used to describe thecontents of the bone density calculating subprogram in a sixthembodiment;

FIG. 11 is a block diagram of the electrical structure of the apparatusfor diagnosing osteoporosis in an eighth embodiment of the presentinvention;

FIG. 12 is a flow chart of the operation and processing procedures ofthe same apparatus;

FIG. 13 schematically depicts the apparatus for diagnosing osteoporosiswhile in use in a ninth embodiment of the present invention;

FIG. 14 is a flow chart of the operation and processing procedures ofthe same apparatus; and

FIG. 15 is a flow chart of the operation and processing procedures ofthe apparatus for diagnosing osteoporosis in a tenth embodiment of thepresent invention.

BEST MODE FOR CARRYING OUT THE INVENTION

The best modes for carrying out the invention are described below withreference to the drawings. The invention is described in detail usingembodiments.

Embodiment 1

FIG. 1 is a block diagram depicting the electrical structure of theapparatus for diagnosing osteoporosis in a first embodiment of theinvention; FIG. 2 is a schematic outer view of the same apparatus; FIGS.3 through 6 are illustrations used to describe the operation of theapparatus; FIG. 7 is a flow chart of the operation of the sameapparatus; FIG. 8 is a graph of the regression line for cortical bonedensity ρ relative to the acoustic impedance Zb, and is used to describethe bone density calculating subprogram constituting the same apparatus.

As shown in FIGS. 1 and 2, the apparatus for diagnosing osteoporosis inthis example comprises: an ultrasonic transducer 1 (hereinafter simplyreferred to as transducer), which emits ultrasonic pulses towardpredetermined cortical bone in a subject at a measuring location inresponse to electrical pulse signals that are input at a predeterminedperiod, and receives echoes (reflected waves) from the surface of thecortical bone and converts them to a reception signal (electricalsignal); an apparatus main unit 2, which carries out the diagnosis ofosteoporosis by supplying electrical pulse signals to the transducer 1and processing the reception signals output from the transducer 1 so asto extract the echo level (reflection wave amplitude) from the corticalbone; and a cable 3 connecting the transducer 1 and apparatus main unit2.

The aforementioned transducer 1 consists primarily of an ultrasonicoscillator 1a having electrode layers on either side of a disk-shapedthickness oscillation type of piezo-electric element of lead zirconatetitanate (PZT) or the like. An ultrasonic delay spacer 1b of apolyethylene bulk or the like is fixed to one of the electrode surfaces(ultrasonic pulse transducer surface) of the ultrasonic oscillator 1a inorder to eliminate the effects of transmission reverberation. Here,cortical bone can be irradiated with nearly flat ultrasonic pulses fromthe transducer surface of the transducer 1 to carry out highly accuratemeasurements, and nearly flat echoes should be reflected from thecortical bone to the transducer surface, so the transducer 1 is ideallyconstructed of a piezo-electric element with a relatively large diskradius to make the transducer surface as wide as possible (in thisexample, the diameter D of the transducer surface is 15 mm). From asimilar perspective, the measuring site that is used should be thecortical bone of the heel, top of the patella, tibia, scapula, cranialbone, or the like, which can be regarded as being flat, with a largecurvature radius, and which is close to the surface of the skin. As aresult of detailed measurements at various locations of cortical bone inhumans, the inventors of the present application found that an idealmeasuring location was the cortical bone of the lower tibia, especiallywithin a range K of 40 mm to 100 mm over the ankle Mc, as shown in FIG.3, because virtually noise-free echoes alone were extractedindependently from the lower tibia Mb far more frequently than with thecortical bone in other locations. When the influence of transmissionreverberation is negligible, the ultrasonic delay spacer 1b can beomitted.

The aforementioned apparatus main unit 2 comprises a pulse generator 4,matching circuit 5, amplifier 6, waveform shaper 7, A/D convertor 8, ROM9, RAM 10, CPU (central processing unit) 11, level meter 12, and display13.

The pulse generator 4 is connected via a cable 3 to the transducer 1,and repeatedly produces an electrical pulse signal with a centralfrequency of, for example, 1 MHz or 2.5 MHz at a predetermined period(100 msec, for example), which is sent to the transducer 1. The matchingcircuit 5 matches impedance, to allow the signals to be transmitted andreceived at optimal energy efficiency between the transducer 1 andapparatus main unit 2 which are connected by the cable 3. Thus, when theultrasonic oscillator 1a of the transducer 1 receives echoes fromcortical bone, the reception signal is output from the transducer 1 andis input to the amplifier 6 via the matching circuit 5 with no loss ofenergy. The amplifier 6 amplifies the reception signal input through thematching circuit to a predetermined amplification level and then inputsit to the waveform shaper 7. The waveform shaper 7 consists of a bandpass filter having an LC structure, and filters the reception signalthat has been amplified by the amplifier 6 to shape the waveform to alinear form in order to eliminate noise, and the signal is then input tothe A/D convertor. The A/D convertor 8 is equipped with a sample holdercircuit not shown in the figure, sampling memory (SRAM), and the like,and samples the output signal from the waveform shaper 7 (waveformshaped analog reception signal) at a predetermined frequency (such as 12MHz) when the CPU 11 sends a command to start sampling, so as tosequentially convert the signals to digital signals, and the resultingdigital signals are temporarily stored in the sampling memory itself andthen sent to the CPU 11.

The ROM 9 stores the operating system (OS) as well as the variousprocessing programs of the CPU 11, specifically, the maximum echo levelextracting subprogram, reflection coefficient calculating subprogram,acoustic impedance calculating subprogram, and bone density calculatingsubprogram.

A procedure for taking in the digital signal from the sampling memory ofthe A/D convertor 8 for each pulse and echo to detect the echo level foreach echo, and a processing procedure for extracting the maximum echolevel from the echo levels that are detected for each echo, are writtento the maximum echo level extraction subprogram. A processing procedurefor calculating the ultrasonic reflection coefficient R during roughlyperpendicular reflection at the interface between the soft tissue andcortical bone (measuring location) of the patient based on the maximumecho level value given by the maximum echo level extraction subprogramis written to the reflection coefficient calculating subprogram. Aprocedure for calculating the acoustic impedance Zb using Formula (5)based on the values calculated for the ultrasonic reflection coefficientR given by the reflection coefficient calculating subprogram is writtento the acoustic impedance calculating subprogram.

    Zb=Za(R+1)/(1-R)                                           (5)

Za: acoustic impedance of soft tissue Formula (5) is derived fromFormula (6). As shown in FIG. 6(a), the surface Y of cortical bone Mbcan be regarded as being flat, and the ultrasonic pulse Ai generatedfrom the transducer 1 can also be regarded as being flat, so when thewavefront is parallel to the surface Y of the cortical bone Mb (landsroughly perpendicular), the ultrasonic reflection coefficient isexpressed by Formula (6). As will be described below, the echo level isgreatest when the wavefront of a flat wave and the surface Y of corticalbone Mb are parallel. Accordingly, the ultrasonic reflection coefficientgiven by Formula (6) is the ultrasonic reflection coefficient when themaximum echo level is obtained. Formula (5) is thus obtained bytransforming Formula (6).

    R=(Zb-Za)/(Zb+Za)                                          (6)

The bone density calculating subprogram contains a processing procedurefor the bone density (cortical bone density) ρ of a patient usingFormula (7) based on the value calculated for the acoustic impedance Zbgiven by the acoustic impedance calculating subprogram.

Here, Formula (7) is the recurrence formula of the bone density ρrelative to the acoustic impedance Zb, which is obtained by priorexamination of a specimen, as shown in FIG. 8. ##EQU1## ρ: cortical bonedensity kg/m³ !Zb: acoustic impedance of cortical bone kg/m² sec!

α: regression coefficient of bone density relative to acoustic impedancesec/m!

β: section kg/m³ !

In the examination of the specimen described above, the acousticimpedance Zb was measured for the cortical bone of the tibia usingultrasonic reflection, and the density ρ of the cortical bone Mb wasmeasured by X-ray (QCT) of the radius (arm bone). Examination of thespecimen revealed a high correlation (r=0.67) between the acousticimpedance Zb and the bone density ρ measured by X-ray (QCT). Statisticalhypothesis testing resulted in a 95% probability (reliability) that apatient's bone density ρ would fall within the ρmin to ρmax range whenthe value for the acoustic impedance Zb of the cortical bone of anypatient is Zb. The significance level is thus 5%.

Here, ρmin is given by Formula (8), and ρmax is given by Formula (9).

    ρmin=(1.80×10.sup.-4 -30%)Zb+(766-16%)           (8)

    ρmax=(1.80×10.sup.-4 +30%)Zb+(766+16%)           (9)

RAM 10 has a working area in which the working area for the CPU 11 isestablished, and a data area in which various data are temporarilystored. The data area contains an echo level memory area for storing themost recently detected echo level (hereinafter referred to as currentecho level) or maximum echo level, an echo waveform memory area forstoring the most recently detected echo waveform (current echo waveform)or maximum echo waveform, and a measurement continue flag or the likefor storing data on whether or not to continue measurement.

The CPU 11 executes the various processing programs stored in the ROM 9using RAM 10 to start the pulse generator 4 or A/D convertor 8, controlsthe various components of the apparatus to detect echo levels for eachpulse and echo, extracts the maximum echo level, and calculates the bonedensity ρ of the patient based on the maximum echo level value detected,so as to diagnose osteoporosis.

The level meter 12 is controlled by the CPU 11 and displays the currentecho level stored in RAM 10 by the deflection of the liquid crystalneedle pattern 12a indicated by the broken line in FIG. 2 as well as themaximum echo level, which is the greatest echo level among those thusfar detected, by the deflection of the liquid crystal needle patten 12bindicated by the solid line in the figure. The display 13 consists of aCRT display or liquid crystal display. The measured values of the echolevels and the like, the ultrasonic reflection coefficient R, theacoustic impedance Zb, the calculated values of the bone density ρ, andthe echo waveforms are displayed on screen under the control of the CPU11.

The operation of this example (course of CPU 11 processing duringdiagnosis of osteoporosis) is described below with reference to FIGS. 4through 7.

First, the cortical bone of the lower tibia, particularly within a rangeK of 40 mm to 100 mm above the ankle Mc, is selected. Of course, thecortical bone of other desirable locations such as the heel, top of thepatella, scapula, and cranial bone may also be selected as needed. Whenthe power source is turned on in the apparatus, the CPU 11 presets thevarious components of the apparatus and initializes the counter, thevarious registers, and the various flags, and waits for the measurementbegin switch to be pressed (step SP10 (FIG. 7)). Here, as shown in FIG.4, the operator applies ultrasonic gel 14 over the surface of the softtissue Ma (skin surface X) on the cortical bone Mb at the patientmeasuring location, presses the transducer 1 against the skin surface Xvia the ultrasonic gel 14, and turns the measurement begin switch on,with the transducer surface facing the cortical bone Mb. When themeasurement begin switch is turned on (step SP11), the CPU 11 writes "1"to the measurement continue flag to raise the measurement continue flag,and the diagnostic operations are then started according to theprocessing procedure (primarily the procedure in the maximum echo levelextraction subprogram) shown in FIG. 7. The CPU 11 first issues a 1pulse generating command to the pulse generator 4 (step SP12). When thepulse generator 4 receives the 1 pulse generating command from the CPU11, it sends an electrical pulse signal to the transducer 1. When thetransducer 1 receives the electrical pulse signal from the pulsegenerator 4, it emits a nearly flat ultrasonic pulse Ai toward thepatient's cortical bone Mb. As shown in FIG. 5, the ultrasonic pulse Aithus emitted is introduced from the skin surface X into the soft tissueMa and is propagated toward the cortical bone Mb. A portion is reflectedat the surface Y of the cortical bone Mb, resulting in echo Ae, and aportion is absorbed by the cortical bone Mb, but the remainder passesthrough the cortical bone Mb. The echo Ae follows a path opposite thatof the incident ultrasonic pulse Ai and is received back at theultrasonic oscillator 1a of the transducer 1. When the ultrasonic pulseAi is emitted from the transducer 1 toward the cortical bone Mb, asshown in the figure, first the transmission resonance An₁, then the echoAn₂ from the skin surface X, and a little later the echo Ae from thecortical bone Mb are received by the ultrasonic oscillator 1a and areconverted to a reception signal (electrical signal) corresponding to theultrasonic waveform and amplitude. The resulting reception signal isinput via the cable 3 to the apparatus main unit 2 (matching circuit 5),amplified to a predetermined amplification level by the amplifier 6,shaped into a linear waveform by the waveform shaper 7, and then inputto the A/D convertor 8.

After the CPU 11 has sent a 1 pulse generating command to the pulsegenerator 4 (step SP12), it issues a sampling start command (step SP13)to the A/D convertor 8 upon measuring the time in which the transmissionresonance An₁ is received by the ultrasonic oscillator 1a of thetransducer 1, the echo An₂ from the skin surface X is then received, andthe echo Ae from the cortical bone Mb returns to the transducer surfaceof the oscillator 1a of the transducer 1.

When the A/D convertor 8 receives the sampling start command from theCPU 11, it samples the reception signal for one echo from the corticalbone Mb, which has been input after undergoing waveform shaping from thewaveform shaper 7, at a predetermined frequency (such as 12 MHz) toconvert it to a digital signal, and the resulting N sample value(digital signal for 1 echo) is temporarily stored in the sample memoryitself. Subsequently, when there is a transmission command from the CPU11, the N sample values stored in the sampling memory are sequentiallytransmitted to the CPU 11. The CPU 11 sequentially takes in the N samplevalues from the A/D convertor 8 and stores the current echo waveform inthe echo waveform memory area of RAM 10, the maximum value among the Nsample values is extracted so as to detect the current echo level, andthe detected results are stored in the echo level memory area of RAM 10(step SP14). The current echo level stored in the echo level memory areaof RAM 10, as shown by the broken line in FIG. 4, is displayed by thedeflection of the liquid crystal needle pattern 12a in the level meter12 (step SP15).

The CPU 11 then reads out the current echo level and the maximum echolevel from the echo level memory area of RAM 10 to determine whether ornot the current echo level value is greater than the maximum echo levelvalue (step SP16). This is the first determination, and since themaximum echo level value is the initialized value "0," the CPU 11determines that the current echo level value is greater than the maximumecho level value, the maximum echo level value stored in the echo levelmemory area of RAM 10 is replaced by the current echo level value, andthe maximum echo waveform stored in the echo waveform memory area of RAM10 is also replaced by the current echo waveform (step SP17). The newmaximum echo waveform is displayed on the screen of the display 13, andthe new maximum echo level is displayed by the deflection of the liquidcrystal needle pattern 12b on the level meter 12, as shown by the solidline in FIG. 4 (step SP18). Then, when the CPU 11 looks for themeasurement continue flag in RAM 10 (step SP19) and raises themeasurement continue flag (when the contents of the measurement flag are"1"), the CPU 11 determines that measurement is to continue, repeats the1 pulse emission and 1 echo reception described above (steps SP12through SP15), and then again reads out the current echo level andmaximum echo level from the echo level memory area in RAM 10 in stepSP16 to determine whether or not the current echo level value is greaterthan the value of the maximum echo level. When it is determined that thecurrent echo level is not greater than the maximum echo level, thesystem jumps directly to step SP19 without modifying the values, andlooks for the measurement continue flag. As long as the operator doesnot press the measurement end switch, the contents of the measurementcontinue flag are "1," and the CPU 11 repeats the 1 pulse emission 1echo transmission described above (steps SP12 through SP15) and themaximum echo level extraction (steps SP16 through SPl9).

While the CPU 11 is repeating the process described above (steps SP12through SP19), the operator aims the transducer 1 at the skin surface X,as indicated by the arrow W in FIG. 4, and changes the direction of thetransducer 1 by sometimes describing a circle in the manner of theprecession of a top and sometimes oscillating it in any direction in themanner of a seesaw on the cortical bone Mb at the measuring site whilechecking the direction in which the liquid crystal needle patterns 12aand 12b of the level meter 12 oscillate the greatest, that is, thedirection in which the maximum echo level is detected. As shown in FIG.6(a), the maximum oscillation of the liquid crystal needle patterns 12aand 12b of the level meter 12 is where the normal of the cortical boneMb and the normal of the transducer surface of the transducer 1 arealigned and thus when the wavefront of the flat ultrasonic pulse Ai isroughly parallel to the surface Y of the cortical bone Mb (when the flatultrasonic pulse Ai lands roughly perpendicular on the surface Y of thecortical bone Mb).

That is because, when both normals are aligned, as shown in FIG. 6(a),the echo Ae reflected perpendicular on the surface Y of the corticalbone Mb returns perpendicular to the transducer surface of thetransducer 1, so the wavefront of the echo Ae is also roughly parallelto the transducer surface. There is thus minimal deviation of the echoAe phase due to differences in the reception position on the transducersurface, so the crests and troughs of the reception signal do not canceleach other out very much, allowing echoes Ae to be received at maximumecho levels. In contrast, when both normals are not aligned, as shown inFIG. 6(b), the wavefront of the echo Ae does not line up with thetransducer surface, so the reception signal is lower because the crestsand troughs cancel each other out.

Diagnostic accuracy is increased in the diagnostic apparatus in thisembodiment, based on the extraction of the perpendicularly reflectedecho Ae. That is because Formula (5) for deriving the acoustic impedanceZb from the ultrasonic reflection coefficient R during roughlyperpendicular reflection in the acoustic impedance calculatingsubprogram described above is established when the echo Ae is reflectedroughly perpendicularly from the cortical bone Mb, as described above.Hence, when the echo level peaks out as the operator varies the angle ofthe transducer 1 around the normal of the cortical bone Mb, it can beconcluded that echoes Ae are reflected roughly perpendicularly on thesurface Y of the cortical bone Mb back to the transducer surface of thetransducer 1.

The liquid crystal patterns 12a and 12b of the level meter 12 change ina sensitive manner (oscillate vigorously) in the event of pronouncednonalignment between the normal of the cortical bone Mb and the normalof the transducer surface, but since such changes are blunted (theoscillation abates) when the normals are roughly aligned, it isrelatively easy to find a perpendicularly reflected echo Ae.

When the operator looks at the extent of oscillation in the liquidcrystal needle patterns 12a and 12b of the level meter and determinesthat the maximum echo level can be extracted, the measurement end switchis pressed. When the measurement end switch is pressed, the CPU 11rewrites the contents of the measurement continue flag as "0" by aninterrupt process so as to lower the measurement continue flag. When themeasurement continue flag is lowered, the CPU 11 stops any subsequent 1pulse emissions (step SP19). The maximum echo level stored in the echolevel memory area of RAM 10 is read out and displayed on the screen ofthe display 13 (step SP20).

The CPU 11 then executes the reflection coefficient calculatingsubprogram to calculate the ultrasonic reflection coefficient R at theinterface between the soft tissue Ma and cortical bone Mb of the patientbased on the maximum echo level V1 stored in the echo level memory areaof RAM 10 and the complete echo level V0 previously written to thereflection coefficient calculating subprogram (step SP21), and thecalculated value is displayed on the screen of the display 13 (stepSP22).

Here, the ultrasonic reflection coefficient R is derived from the ratioR=V1/V0! between the complete echo level V0 during completelyperpendicular reflection and the maximum echo level V1. The completeecho level V0 can be calculated theoretically, but it can also bedetermined by preparing a dummy block made of plastic or the like tomeasure the echo levels.

The CPU 11 then substitutes the value for the ultrasonic reflectioncoefficient R given by the reflection coefficient calculating subprograminto Formula (5) to calculate the acoustic impedance Zb kg/m² sec! ofthe cortical bone Mb in accordance with the acoustic impedancecalculating subprogram (step SP23), and the results of the calculationare displayed on the screen of the display 13 (step SP24). The CPU 11then substitutes the value for the acoustic impedance Zb of the corticalbone Mb given by the acoustic impedance calculating subprogram intoFormula (7) to calculate the bone density in accordance with the bonedensity calculating subprogram (step SP25), and the results of thecalculation are displayed on the screen of the display 13 (step SP26).

Thus, in the structure described above, the maximum echo level is easilyextracted, with good extraction reproducibility, because of the use ofperpendicularly reflected echoes Ae in which the changes in echo levelsfrom the cortical bone due to displacement (oscillation of thetransducer 1) are blunted. Because the cortical bone of the lower tibiais used as a measuring location, there is less contamination by noise ofunknown origin, thus ensuring reliable detection of echoes from thecortical bone. In addition, the current echo levels are displayed momentby moment by the liquid crystal needle pattern 12a of the level meter12, and the maximum echo level is also constantly displayed by theliquid crystal needle pattern 12b, so the maximum echo level is easy tofind. The acoustic impedance Zb of the cortical bone Mb can thus also beaccurately determined.

The acoustic impedance Zb of the cortical bone Mb is expressed by thesquare root of the elastic modulus×density! of cortical bone Mb, andthus increases with extreme sensitivity in response to increases in thecortical bone density as a result of the synergistic effects in whichthe elastic modulus of cortical bone increases as the cortical bonedensity increases. Similarly, the elastic modulus of cortical bonedecreases with decreases in cortical bone density, so the acousticimpedance Zb decreases with extreme sensitivity in response to decreasesin cortical bone density. The acoustic impedance Zb of cortical bone Mbis thus a good index for determining bone density.

Furthermore, a recurrence formula for bone density ρ relative toacoustic impedance Zb has also been prepared, allowing the bone density(cortical bone density) ρ of a patient to be calculated with a 95%reliability based on the acoustic impedance Zb. The extent ofosteoporosis can thus be directly ascertained.

Embodiment 2

A second embodiment of the present invention is described below.

The reflection coefficient calculating subprogram (algorithm) used inthe second embodiment is different from that in the first embodimentdescribed above. Other than this, the embodiment is roughly the same instructure as the first embodiment. That is, in the reflectioncoefficient calculating subprogram in the second embodiment, theultrasonic reflection coefficient R for when the ultrasonic pulse Ai isroughly perpendicularly reflected at the interface between the softtissue Ma and cortical bone Mb can be determined using Formula (10),assuming that the ultrasonic pulse Ai and echo Ae are regarded as beingsufficiently flat and that the attenuation of the ultrasonic waves inthe soft tissue Ma can be disregarded.

    R=Ve/P·Q·B·Vi                   (10)

R: ultrasonic reflection coefficient for when ultrasonic pulse Ai isroughly perpendicularly reflected at the interface between soft tissueMa and cortical bone Mb

P: sound pressure of ultrasonic pulse Ai output from transducer 1 inroughly perpendicular direction When unit electrical signal (voltage,current, scattering parameter, or the like) is applied to transducer 1

Q: amplitude of reception signal (electrical signal) output fromtransducer 1 when unit sound pressure of echo Ae lands roughlyperpendicular on transducer surface of transducer 1

B: product of amplification level amplifier 6 and amplification level ofwaveform shaper 7

Vi: amplitude of electrical signal applied from pulse generator 4 totransducer 1

Ve: maximum echo level

P, Q, B, and Vi are all functions of frequency. Components at a centralfrequency (such as 2.5 MHz) are used here. The measured and set valuesfor P, Q, B, and Vi are previously written to ROM 9 (the reflectioncoefficient calculating subprogram in this example).

Formula (10) is derived as follows. First, when an electrical signal ofamplitude Vi is applied from the pulse generator 4 to the transducer 1,an ultrasonic pulse Ai of sound pressure PVi is output from thetransducer surface of the transducer 1 toward the cortical bone Mb. As aresult, a bone echo Ae of sound pressure RPVI is returnedperpendicularly to the transducer surface of the transducer 1. Themaximum echo level Ve is accordingly given by Formula (11).

    Ve=Q·R·P·B·Vi          (11)

Formula (10) is derived from Formula (11).

Roughly the same effects as those in the first embodiment can thus alsobe obtained in the second embodiment because the acoustic impedance Zbof cortical bone Mb is calculated by the CPU 11 from the ultrasonicreflection coefficient R at the interface between soft tissue Ma andcortical bone Mb.

Embodiment 3

A third embodiment of the present invention is described below.

The third embodiment differs from the first embodiment in that ρmin toρmax is calculated and output with a 95% reliability or 5% significancelevel when the bone density calculating subprogram is executed to carryout the regression of the bone density ρ. Other than this, theembodiment is roughly the same in structure as the first embodiment.That is, Formula (12) is used as a recurrence formula giving the bonedensity ρ in the bone density calculating subprogram in this example.

    ρ=αZb+β                                     (12)

ρ: cortical bone density kg/m³ !

Zb: acoustic impedance of cortical bone (kgm² sec!

α: regression coefficient sec/m!

β: section kg/m³ !

Formula (12) differs from Formula (5) in the first embodiment describedabove in that the value of the regression coefficient a has a widerrange from 1.27×10⁻⁴ to 2.34×10⁻⁴, and the value for section β has awider range from 646 to 887.

As such, the bone density ρmin to ρmax that is determined is also wider.##EQU2##

Expressed in percentage, Formulas (13) and (14) are the same as Formulas(8) and (9) in the first embodiment, and it may be seen that therecurrence formula in the first embodiment is the equivalent of thecenterline of the wider range of the recurrence formula in the thirdembodiment. As a result, the patient's bone density ρ has a 95%probability (reliability) and 5% significance level of falling withinthe ρmin to ρmax range when the acoustic impedance Zb value for thecortical bone of any patient is Zb. The same specimen analysis data asthat used in the first embodiment is used to derive the recurrenceformula in the third embodiment, so the bone density ρ calculated byX-ray (QCT) has a high correlation (r=0.67) with the acoustic impedanceZb in the third embodiment as well.

Thus, roughly the same effects as in the first embodiment above can beobtained with the structure of this example, allowing the estimatedvalue of the bone density ρ to be assessed in terms of probability(statistics).

Embodiment 4

A fourth embodiment of the present invention is described below.

The structure of the fourth embodiment differs substantially from thestructure of the first through third embodiments in that a linearrecurrence formula (ρ=αZb+β) was used in the bone density calculatingsubprograms of the first through third embodiments, whereas a nonlinearrecurrence formula, as indicated in Formula (15), is used in the fourthembodiment. Here, Formula (15) is a recurrence formula for bone densityρ relative to the acoustic impedance Zb, and, as shown in FIG. 9, isobtained by the statistical treatment of data from the specimenexamination.

    ρ=BZb.sup.A =10.sup.0.894 Zb.sup.0.342                 (15)

ρ: cortical bone density kg/m³ !

Zb: acoustic impedance of cortical bone kg/m² sec!

A: regression index

B: constant sec/m!

Statistical hypothesis testing resulted in a 95% probability(reliability) that a patient's bone density ρ would fall within the ρminto ρmax range when the value for the acoustic impedance Zb of thecortical bone of any patient is Zb. The significance level is thus 5%.Here, ρmin is given by Formula (16), and ρmax is given by Formula (17).

    ρmin=10.sup.(0.894-73%) Zb.sup.(0.342-30%)             (16)

    ρmax=10.sup.(0.894+73%) Zb.sup.(0.342+30%)             (17)

The same specimen analysis data as that used in the first embodiment isused to derive the recurrence formula in the fourth embodiment, so thebone density ρ calculated by X-ray (QCT) has a high correlation (r=0.67)with the acoustic impedance Zb in the fourth embodiment as well. Thus,roughly the same effects as in the first embodiment above can beobtained with the structure of this example.

Embodiment 5

The fifth embodiment differs from the fourth embodiment in that ρmin toρmax is calculated and output with a 95% reliability or 5% significancelevel when the bone density calculating subprogram is executed to carryout the regression of the bone density ρ. Other than this, theembodiment is roughly the same in structure as the fourth embodiment.That is, Formula (18) is used as a recurrence formula giving the bonedensity ρ in the bone density calculating subprogram in this example.

    ρ=BZb.sup.A =10.sup.0.894 Zb.sup.0.342                 (18)

ρ: cortical bone density kg/m³ !

Zb: acoustic impedance of cortical bone kg/m² sec!

A: regression index

B: constant sec/m!

Formula (18) differs from Formula (15) in the fourth embodiment in thatthe value of the regression index A has a wider range of 0.239 to 0.445,and the value of the constant B also has a wider range of 10⁰.239 to10¹.55. As such, the bone density ρmin to ρmax that is determined alsohas a wider range. ##EQU3##

Expressed in percentage, Formulas (19) and (20) are the same as Formulas(16) and (17) in the fourth embodiment, and it may be seen that therecurrence formula in the fourth embodiment is the equivalent of thecenterline of the wider range of the recurrence formula in the fifthembodiment. As a result, the patient's bone density ρ has a 95%probability (reliability) and 5% significance level of falling withinthe ρmin to ρmax range when the acoustic impedance Zb value for thecortical bone of any patient is Zb. The same specimen analysis data asthat used in the first embodiment is used to derive the recurrenceformula in the fifth embodiment, so the bone density ρ calculated byX-ray (QCT) has a high correlation (r=0.67) with the acoustic impedanceZb in the fifth embodiment as well.

Thus, roughly the same effects as in the first embodiment above can beobtained with the structure of this example, allowing the estimatedvalue of the bone density ρ to be assessed in terms of probability(statistics).

Embodiment 6

A sixth embodiment of the present invention is described below.

The structure of the sixth embodiment differs substantially from thestructure of the first through fifth embodiments in that the patient'sbone density is calculated using a predetermined recurrence formula forbone density ρ relative to acoustic impedance Zb in the bone densitycalculating subprogram in the first through fifth embodiments, whereasthe patient's bone density ρ is calculated using a recurrence formulafor bone density ρ relative to the ultrasonic reflection coefficient Rin the bone density calculating program in the sixth embodiment. Here,Formula (21) is a recurrence formula for bone density ρ relative to theultrasonic reflection coefficient R, and, as shown in FIG. 10, isobtained by the statistical treatment of data from the specimenexamination.

    ρ=α'R+β'=843R+1000                          (21)

ρ: cortical bone density kg/m³ !

R: ultrasonic reflection coefficient at interface between soft tissueand cortical bone

α': regression coefficient kg/m³ !

β': section kg/m³ !

In the specimen examination described above, the ultrasonic reflectioncoefficient R was calculated for the cortical bone of the tibia usingultrasonic reflection, and the density ρ of the cortical bone Mb wasdetermined by X-ray (QCT) of the radius (arm bone). Specimen analysisrevealed that the bone density measured by X-ray (QCT) had a highcorrelation (r=0.67) with the ultrasonic reflection coefficient R.

Statistical hypothesis testing resulted in a 95% probability(reliability) that a patient's bone density ρ would fall within the ρminto ρmax range when the value for the ultrasonic reflection coefficient Rof the cortical bone of any patient is R. The significance level is thus5%.

Here, ρmin and ρmax are given by Formulas (22) and (23), respectively.

    ρmin=(843-30%)R+(1000-6%)                              (22)

    ρmin=(843+30%)R+(1000+6%)                              (23)

The same specimen analysis data as that used in the first embodiment isused to derive the recurrence formula in the sixth embodiment, so thebone density ρ calculated by X-ray (QCT) has a high correlation (r=0.67)with the acoustic impedance Zb in the sixth embodiment as well. Thus,roughly the same effects as in the first embodiment above can beobtained using the ultrasonic reflection coefficient R at the interfacebetween the soft tissue Ma and cortical bone Mb, which is a monotoneincreasing function of the acoustic impedance Zb of cortical bone Mb, asan index of bone density instead of using the acoustic impedance Zb ofcortical bone MB as an index of bone density ρ.

Embodiment 7

The seventh embodiment differs from the sixth embodiment in that ρmin toρmax is calculated and output with a 95% reliability or 5% significancelevel when the bone density calculating subprogram is executed to carryout the regression of the bone density ρ. Other than this, theembodiment is roughly the same in structure as the sixth embodiment.That is, Formula (24) is used as a recurrence formula giving the bonedensity ρ in the bone density calculating subprogram in this example.

    ρ=α'R+β'                                    (24)

ρ: cortical bone density kg/m³ !

R: ultrasonic reflection coefficient at interface between soft tissueand cortical bone

α': regression coefficient kg/m³ !

β': section kg/m³ !

Formula (24) differs from Formula (21) in the sixth embodiment in thatthe value of the regression coefficient α' has a wider range from 588 to1100, and the value for section β' has a wider range from 953 to 1060.As such, the bone density ρmin to ρmax that is determined is also wider.##EQU4##

Expressed in percentage, Formulas (25) and (26) are the same as Formulas(22) and (23) in the sixth embodiment, and it may be seen that therecurrence formula in the sixth embodiment is the equivalent of thecenterline of the wider range of the recurrence formula in the seventhembodiment. As a result, the patient's bone density ρ has a 95%probability (reliability) and 5% significance level of falling withinthe ρmin to ρmax range when the acoustic impedance Zb value for thecortical bone of any patient is Zb. The same specimen analysis data asthat used in the first embodiment is used to derive the recurrenceformula in the seventh embodiment, so the bone density ρ calculated byX-ray (QCT) has a high correlation (r=0.67) with the acoustic impedanceZb in the seventh embodiment as well. Thus, roughly the same effects asin the first embodiment above can be obtained with the structure of thisexample, allowing the estimated value of the bone density ρ to beassessed in terms of probability (statistics).

Embodiment 8

FIG. 11 is a block diagram of the electrical structure of the apparatusfor diagnosing osteoporosis in an eighth embodiment of the presentinvention, and FIG. 12 is a flow chart of the operation and processingprocedures of the same apparatus.

The structure of the apparatus for diagnosing osteoporosis in the eighthembodiment differs substantially from the structure of the first throughseventh embodiments described above by having a Fourier transformfunction, allowing the complex acoustic impedance to be calculated.

As shown in FIG. 11, the apparatus main unit 2A in this example has anew timing circuit 15 in addition to the structure of the firstembodiment.

The pulse generator 4 repeatedly produces an electrical pulse signal of1 MHz or 2.5 MHz, for example, at a predetermined period (100 msec, forexample) and transmits these pulses to the transducer 1, and a timingstart signal Tp is supplied to the timing circuit 15 with the sametiming as that in the transmission of the electrical pulse signal. Theultrasonic pulse period is set sufficiently longer than the echo arrivaltime described below.

The following processing program is stored in the ROM 9 in this exampleto allow the CPU 11 to calculate the complex acoustic impedance in orderto diagnose osteoporosis. That is, the processing program in thisexample includes: a procedure in which the echo waveform (echo signal)is taken from the A/D converter 8 for each pulse and echo so as to checkthe echo level; a procedure in which the maximum echo level is extractedfrom the many echo levels thus detected; a processing procedure in whichthe high speed Fourier transform means is actuated to rapidly determinethe maximum echo waveform spectrum on the basis of the maximum echowaveform during the extraction of the maximum echo level; a procedure inwhich the ultrasonic complex reflection coefficient R(ω) of the corticalbone Mb relative to the soft tissue Ma of the patient at an angularfrequency ω is calculated based on the spectrum; and a procedure inwhich the complex acoustic impedance Zb(ω) of the patient's corticalbone Mb at an angular frequency ω is calculated based on the ultrasoniccomplex reflection coefficient R(ω) thus calculated.

In this processing program, the complex acoustic impedance Zb(ω) for thepatient's cortical bone Mb is given by Formula (27).

    Zb(ω)=Za(ω){R)ω)+1}/{1-R(ω)}       (27)

Za(ω): complex acoustic impedance (known) of soft tissue Ma at angularfrequency ω

R(ω): ultrasonic complex reflection coefficient of cortical bone Mbrelative to soft tissue Ma of patient at angular frequency ω

Formula (27) is derived from Formula (28). That is, as shown in FIG.6(a), the ultrasonic complex reflection coefficient R(ω) of the corticalbone Mb relative to the soft tissue Ma of the patient is expressed byFormula (28) when the surface Y of the cortical bone Mb is roughly flat,the ultrasonic pulse Ai emitted from the transducer 1 is also flat, andthe wavefront is roughly parallel to the surface Y of the cortical boneMb (in other words, when the ultrasonic pulse Ai lands roughlyperpendicular on the surface Y of the cortical bone Mb). Meanwhile, theecho level is greatest when the ultrasonic pulse Ai lands roughlyperpendicular on the surface Y of the cortical bone Mb. As such, theultrasonic complex reflection coefficient R(ω) given by Formula (28) isthe ultrasonic complex reflection coefficient R(ω) when the maximum echolevel is obtained. Formula (27) is thus obtained by the rearrangement ofFormula (28).

    R(ω)={Zb(ω)-Za(ω)}/{Zb(ω)+Za(ω)}(28)

The CPU 11 uses RAM 10 to execute the processing program described abovestored in ROM 9 so as to start the pulse generator 4 or A/D convertor 8,controls each component of the apparatus to take in an echo signal fromthe A/D convertor 8 for each pulse and echo to detect the echo level,extracts the maximum echo level, determines the maximum echo waveformspectrum based on the maximum echo waveform, calculates the ultrasoniccomplex reflection coefficient R(ω) of the cortical bone Mb relative tothe soft tissue Ma of the patient at an angular frequency (ω) on thebasis of the spectrum, calculates the complex acoustic impedance Zb(ω)of the patients' cortical bone Mb at the angular frequency ω based onthe ultrasonic complex reflection coefficient R(w) thus calculated, andproduces a diagnosis of osteoporosis on the basis of the phase data andamplitude data obtained form the complex acoustic impedance thuscalculated. The measured values of the echo levels and the like, theultrasonic complex reflection coefficient R(ω), the complex acousticimpedance Zb(ω), the calculated value for bone density ρ, the echowaveform, and the like are displayed on the screen of the display 13under the control of the CPU 11. The timing circuit 15 measures the echoarrival time, which is the time elapsed after the ultrasonic pulse Ai isemitted from the transmitting surface of the transducer 1 until the echoAe is reflected on the surface Y of the cortical bone Mb back to thereceiving surface. The timing circuit 15 comprises a clock generator andcounter circuit which are not shown in the figure, wherein the timing isstarted whenever a timing start signal Tp is received from the pulsegenerator 4, and the timing is concluded when a stop signal is sent fromthe A/D convertor 8. Here, the transmission of the stop signal from theA/D convertor 8 is the timing by which the A/D convertor 8 detects thereception of the echo Ae. The timing value is thus kept until it isreset, and the timing value that is kept is given to the CPU 11 as theecho arrival time as needed.

The operation of this example (primarily the CPU 11 processing duringthe diagnosis of osteoporosis) is described below with reference to FIG.12.

First, the cortical bone Mb of the tibia, for example, which has asubstantial curvature radius, which is close to the surface of the skin,and which is relatively thick, is selected as the measuring site.

When the power source is turned on in the apparatus, the CPU 11 presetsthe various components of the apparatus and initializes the counter, thevarious registers, and the various flags (step SQ10), and then waits forthe measurement begin switch to be pressed (step SQ11). Here, as shownin FIG. 4, the operator applies ultrasonic gel 14 over the surface ofthe soft tissue Ma (skin surface X) on the cortical bone Mb at thepatient measuring location, presses the transducer 1 against the skinsurface X via the ultrasonic gel 14, and turns the measurement beginswitch on, with the transducer surface facing the cortical bone Mb. Whenthe measurement begin switch is turned on (step SQ11), the CPU 11 writes"1" to the measurement continue flag to raise the measurement continueflag, and the diagnostic operations are then started according to theprocessing procedure given in FIG. 12.

The CPU 11 first issues a 1 pulse generating command to the pulsegenerator 4 (step SQ12). When the pulse generator 4 receives the 1 pulsegenerating command from the CPU 11, it sends an electrical pulse signalto the transducer 1, and a timing start signal Tp is supplied to thetiming circuit 15 with the same timing as the transmission of theultrasonic pulse.

When the transducer 1 receives the electrical pulse signal from thepulse generator 4, it emits an ultrasonic pulse Ai (which may beregarded as being flat during the short period of treatment) toward thepatient's cortical bone Mb. Meanwhile, the timing circuit 15 beginstiming at the same time that the timing start signal Tp is received fromthe generator 4. As shown in FIG. 5, a portion of the ultrasonic pulseAi thus emitted from the transducer 1 is reflected at the surface X ofthe skin, and the remainder is introduced from the surface X of the skininto the soft tissue Ma and is propagated toward the cortical bone Mb. Aportion is reflected at the surface Y of the cortical bone Mb, resultingin echo Ae, and a portion is absorbed by the cortical bone Mb, while theremainder passes through the cortical bone Mb. The echo Ae from thecortical bone Mb follows a path opposite that of the incident ultrasonicpulse Ai and is received back at the ultrasonic oscillator 1a of thetransducer 1. After the emission of the ultrasonic pulse Ai by thetransducer 1, first the transmission resonance An₁, then the echo An₂from the skin surface X, and a little later the echo Ae from thecortical bone Mb are received by the ultrasonic oscillator 1a and areconverted to a reception signal corresponding to the ultrasonic waveformand amplitude. The resulting reception signal is input via the cable 3to the apparatus main unit 2 (matching circuit 5), amplified to apredetermined amplification level by the amplifier 6, shaped into alinear waveform by the waveform shaper 7, and then input to the A/Dconvertor 8.

After the CPU 11 has sent a 1 pulse generating command to the pulsegenerator 4 (step SQ12), it issues a sampling start command (step SQ13)to the A/D convertor 8 upon measuring the time in which the transmissionresonance An₁ is received by the ultrasonic oscillator 1a of thetransducer 1, the echo An₂ from the skin surface is then received, andthe echo Ae from the cortical bone Mb returns to the transducer surfaceof the ultrasonic oscillator 1a of the transducer 1. When the A/Dconvertor 8 receives the sampling start command from the CPU 11, itsamples the reception signal for one echo from the cortical bone Mb,which has been input after undergoing waveform shaping from the waveformshaper 7, at a predetermined frequency (such as 12 MHz) to convert it toa digital signal, and the resulting N sample value (digital signal for 1echo) is temporarily stored in the sample memory itself. A stop signalis meanwhile sent to the timing circuit 15, and the timing is stopped.Subsequently, when there is a transmission command from the CPU 11, theN sample values stored in the sampling memory are sequentiallytransmitted to the CPU 11. The CPU 11 sequentially takes in the N samplevalues from the A/D convertor 8 and stores the current echo waveform inthe waveform memory area of RAM 10, the maximum value among the N samplevalues is extracted to detect the current echo level (current echoamplitude), and the detected results are stored in the echo data memoryarea of RAM 10 (step SQ14). Meanwhile, the echo arrival time is readfrom the timing circuit 15 when the echo signal is read in, and thecurrent echo arrival time thus read in is stored in the data memory areaof the RAM 10. The current echo level stored in RAM 10, as shown by thebroken line in FIG. 4, is displayed by the deflection of the liquidcrystal needle pattern 12a in the level meter 12 (step SQ15).

The CPU 11 then reads out the current echo level and the maximum echolevel from the echo data memory area of RAM 10 to determine whether ornot the current echo level value is greater than the maximum echo levelvalue (step SQ16). This is the first determination, and since themaximum echo level value is the initialized value "0," the CPU 11determines that the current echo level value is greater than the maximumecho level value, the maximum echo level value stored in the echo datamemory area of RAM 10 is replaced by the current echo level value, themaximum echo arrival time corresponding to the maximum echo level isreplaced by the current echo arrival time, and the maximum echo waveformstored in the waveform memory area of RAM 10 is also replaced by thecurrent echo waveform (step SQ17).

The new maximum echo waveform is displayed on the screen of the display13, and the new maximum echo level is displayed by the deflection of theliquid crystal needle pattern 12b on the level meter 12, as shown by thesolid line in FIG. 4 (step SQ18). Then, when the CPU 11 looks for themeasurement continue flag in RAM 10 (step SQ19) and raises themeasurement continue flag (when the contents of the measurement flag are"1"), the CPU 11 determines that measurement is to continue, repeats the1 pulse emission and 1 echo reception described above (steps SQ12through SQ15), and then again reads out the current echo level andmaximum echo level from the echo data memory area in RAM 10 in step SQ16to determine whether or not the current echo level value is greater thanthe value of the maximum echo level. When it is determined that thecurrent echo level is not greater than the maximum echo level, thesystem jumps directly to step SQ19 without modifying the values, andlooks for the measurement continue flag.

As long as the operator does not press the measurement end switch, thecontents of the measurement continue flag are "1," and the CPU 11repeats the 1 pulse emission 1 echo transmission described above (stepsSQ12 through QP15) and the maximum echo level extraction (steps SQ16through SQ19). While the CPU 11 is repeating the process described above(steps SQ12 through SQ19), the operator aims the transducer 1 at theskin surface X, as indicated by the arrow W in FIG. 4, and changes thedirection and angle of the transducer 1 by sometimes describing a circleor spiral in the manner of the precession of a top and sometimesoscillating it in any direction in the manner of a seesaw on thecortical bone Mb at the measuring site while checking the direction inwhich the liquid crystal needle patterns 12a and 12b of the level meter12 oscillate the greatest, that is, the direction in which the maximumecho level is detected. As described in the first embodiment, echoes Aereflected roughly perpendicularly at the surface Y of the cortical boneMb can be considered to have returned to the transducer surface of thetransducer 1 when the echo level is greatest. Thus, the echo arrivaltime Ta during the maximum level measured at this time is the time theecho An₂ perpendicularly reflected at the surface Y of the cortical boneMb takes to return to the transducer surface of the transducer 1 afterthe ultrasonic pulse Ai has been emitted. The liquid crystal patterns12a and 12b of the level meter 12 change in a sensitive manner(oscillate vigorously) in the event of pronounced nonalignment betweenthe normal of the cortical bone Mb and the normal of the transducersurface, but since such changes are blunted (the oscillation abates)when the normals are roughly aligned, it is relatively easy to find aperpendicularly reflected echo Ae.

When the operator looks at the extent of oscillation in the liquidcrystal needle patterns 12a and 12b of the level meter and determinesthat the maximum echo level can be extracted, the measurement end switchis pressed. When the measurement end switch is pressed, the CPU 11rewrites the contents of the measurement continue flag as "0" by aninterrupt process so as to lower the measurement continue flag. When themeasurement continue flag is lowered, the CPU 11 stops any subsequent 1pulse emissions (step SQ19). The maximum echo level stored in the echodata memory area of RAM 10 is read out and displayed on the screen ofthe display 13 (step SQ20).

The CPU 11 then moves to a high speed Fourier transform routine, readsout the maximum echo waveform ve(t) from the waveform memory area in RAM10 for Fourier transformation, and determines the maximum echo waveformspectrum (hereinafter referred to as maximum echo spectrum). The maximumecho spectrum Ve(ω) is converted to a frequency f, for example, todetermine the frequency components within a range from about 300 kHz to2.5 MHz. The complex reflection coefficient calculating routine is thenexecuted so as to calculate the ultrasonic complex reflectioncoefficient R(ω) (step SQ21) at the interface between the soft tissue Maand cortical bone Mb of the patient at an angular frequency ω based onthe maximum echo spectrum Ve(ω) thus calculated, and the calculatedvalue is displayed on the screen of the display 13 (step SQ22).

In step SQ21, the ultrasonic complex reflection coefficient R(ω) isgiven by Formula (29). ##EQU5## j: imaginary unit Ve(ω): maximum echospectrum for echo Ae perpendicularly reflected at surface Y of corticalbone Mb

Ta: echo arrival time during maximum level of echo Ae perpendicularlyreflected at surface Y of Cortical bone Mb

Vu(ω): maximum echo spectrum (known) of echo perpendicularly reflectedat pseudo-cortical bone

Tu: echo arrival time (known) during maximum level of echoperpendicularly reflected at pseudo-cortical bone

Ru(ω): ultrasonic complex reflection coefficient (known) ofpseudo-cortical bone relative to pseudo-soft tissue Ma at angularfrequency ω

Here, exp {-jω(Ta-Tu)} is a factor expressing the phase differencebetween an echo Ae from the surface Y of the cortical bone Mb and anecho Au from the surface of the pseudo-cortical bone, which are eachreceived at the transducer surface of the transducer 1, and is intendedto compensate for the difference between the thickness of the softtissue Ma of the patient and the standard thickness of pseudo-softtissue during the measurement of the pseudo-cortical bone.

A substance having acoustic properties similar to those of cortical boneMb (in this case, an acrylic resin) may be used as the pseudo-corticalbone. A substance having acoustic properties similar to those of softtissue Ma (in this case, water) may be used as the pseudo-soft tissueplaced directly in front of the pseudo-cortical bone. The values for themaximum echo spectrum Vu(ω) for pseudo-cortical bone and echo arrivaltime Tu during the maximum level are obtained by previously introducingan acrylic resin block (pseudo-cortical bone) having a known ultrasoniccomplex reflection coefficient Ru(ω) in a water tank (pseudo-softtissue), arranging the transducer 1 at a distance corresponding to thestandard thickness of the soft tissue Ma with respect to the block,emitting ultrasonic pulses Ai at the pseudo-cortical bone, and effectingthe Fourier transform process described above or the like on the echodata thus obtained. The resulting values for the maximum echo spectrumVu(ω) for pseudo-cortical bone and echo arrival time Tu during themaximum level are stored in ROM 9 along with the known ultrasoniccomplex reflection coefficient Ru(ω).

The CPU 11 then executes the complex acoustic impedance calculatingroutine so as to calculate the complex acoustic impedance Zb(ω) forcortical bone Mb by substituting the ultrasonic complex reflectioncoefficient R(ω) given by the complex reflection coefficient calculatingroutine into Formula (27) (step SQ23).

When the patient's osteoporosis is advanced, resulting in|Za(ω)|>|Zb(ω)|!, the real part of R(ω), from Formula (28), is negative.This means that the phase of echo Ae is inverted at the surface Y of thecortical bone Mb. The CPU 11 displays the calculated results of thecomplex acoustic impedance Zb(ω) for cortical bone Mb on the screen ofthe display 13 (step SQ 24).

The acoustic impedance of bone is given by the square root of elasticmodulus×density! of bone, and the elastic modulus of bone increases (ordecreases) with increases (or decreases) in bone density, so the elasticmodulus of bone and bone density play a synergistic role in acousticimpedance. Thus, because the acoustic impedance serves as an index ofosteoporosis in the structure of this embodiment, it is capable ofsensitive response to the extent to which osteoporosis has progressed.For example, when the acoustic impedance of cortical bone is far lowerthan the mean value for a given age level, the osteoporosis of thecortical bone can be considered to have deteriorated.

Furthermore, from Formula (29), phase data can be determined along withthe magnitude of the ultrasonic complex reflection coefficient R(ω), sothe diagnosis will not be erroneous even when the acoustic impedance ofcortical bone is lower than the acoustic impedance for soft tissue. Incontrast, in methods where the reflection coefficient R is not given inthe form of complex numbers, the diagnosis is sometimes erroneousbecause in such cases the CPU 11 takes an absolute value |R| for theultrasonic reflection coefficient R in calculations using Zb=Za(1+|R|)/(1-|R|)=Za (1-R)/(1+R) ! (Formula (5)).

Embodiment 9

FIG. 13 schematically depicts the apparatus for diagnosing osteoporosiswhile in use in a ninth embodiment of the present invention, and FIG. 14is a flow chart of the operation and processing procedures of the sameapparatus.

The complex acoustic impedance could not be calculated unless thecortical bone was of a certain thickness in the apparatus for diagnosingosteoporosis in the eighth embodiment, whereas a feature of theapparatus for diagnosing osteoporosis in this example is that even thincortical bone (such as the thin heel bone, which is immediately adjacentto cancellous bone Mc on the side opposite the soft tissue Ma) can beselected as a measuring site.

Echoes produced in cortical bone that is not thick are different fromthose produced in cortical bone of a certain thickness. In cortical bonethat is not thick, as shown in FIG. 13, a portion of the ultrasonicpulse Ai emitted at the cortical bone Mb is reflected at a reflectioncoefficient Sb at the surface Y, resulting in echo Ae0, and a portionpasses through at a transmission coefficient Tb in the form of atransmission ultrasonic wave At0, penetrating the cortical bone Mb andarriving at the interface Q with cancellous bone Mc. At the interface Qwith the cancellous bone Mc, a portion of the transmission ultrasonicwave At0 is reflected at a reflection coefficient Sc, resulting in areflected ultrasonic wave Ar1, and returns through the cortical bone Mb.A portion of the reflected ultrasonic wave Ar1 passes through theinterface Y with soft tissue Ma at a transmission coefficient Tb,resulting in an echo Ae1 toward the transducer 1, and a portion isreflected at the interface Y with the soft tissue Ma, resulting in areflected ultrasonic wave Ar2, and arrives back at the interface Q withthe cancellous bone Mc. A portion of the reflected ultrasonic wave Ar2is reflected here again, resulting in a reflected ultrasonic wave Ar3,and returns through the cortical bone Mb, and a portion passes throughthe interface Y with the soft tissue Ma at a transmission coefficientTb, resulting in an echo Ae1 toward the transducer 1. Accordingly, theecho Ae returning from the cortical bone Mb involves an overlapping ofechoes Ae0, Ae1, Ae2, etc. which are obtained in the course of themultiple reflections described above. The ultrasonic complex reflectioncoefficient R(ω) of the patient's bone is thus given by Formula (30).##EQU6## τ: time for ultrasonic wave to propagate through cortical boneMb of a thickness L

In the case of perpendicular incidence, Formulas (31) and (32) are usedfor the interface Y between cortical bone Mb and soft tissue Ma, andFormula (33) is used for the interface Q between the cancellous bone Mcand cortical bone Mb.

    Sb(ω)={Zb(ω)-Za(ω)}/{Zb(ω)+Za(ω)}(31)

    Tb(ω)=2{Zb(ω)Za(ω)}.sup.1/2 /{Zb(ω)+Za(ω)}(32)

    Sc(ω)={Zc(ω)-Zb(ω)}/{Zc(ω)+Zb(ω)}(33)

Zc: complex acoustic impedance for cancellous bone Mc

Formulas (31), (32), and (33) are each substituted into Formula (30),and are arranged when the thickness L of the cortical bone Mb issufficiently smaller than the ultrasonic wavelength to obtain Formula(34) giving the complex acoustic impedance Z(ω) which takes into accountthe multiple echoes Ae0, Ae1, Ae2, etc. ##EQU7##

As shown in Formula (35), Formula (34) is simplified when taking intoaccount Zb(ω)>>Zc(ω).

    Z(ω)=Zc(ω)+jωτZb(ω)=Zc(ω)+jωρL(35)

ρ: bone density of cortical bone Mb

Here, ρL is the mass per unit surface area of cortical bone Mb, that is,the area density σ.

Although the complex acoustic impedance Z(ω) of bone can be calculatedon the basis of echo data in conformance with Formula (27), the real andimaginary parts of Formulas (27) and (35) are equal, so the complexacoustic impedance Zc(ω) of cancellous bone Mc can be determined fromthe real parts, and the area density σ of the cortical bone Mb can bedetermined from the imaginary parts. In this case, the bone density ρ ofthe cortical bone Mb can be determined if the thickness L of thecortical bone Mb is known. The processing program in this exampleincludes Formula (35) and the like, and takes into account the multipleechoes Ae0, Ae1, Ae2, etc.

The operation of this example (primarily the CPU 11 processing duringthe diagnosis of osteoporosis) is described below with reference to FIG.14.

Steps SR10 to SR20 in the processing in this example are roughly thesame as those in the eighth embodiment (steps SQ10 to SQ20 (FIG. 12)),so the description here will begin with step SR20 for the sake ofconvenience.

The CPU 11 displays the maximum echo level on the screen of the display13 (step SR20), and then advances to step SR201 and executes the highspeed Fourier transform routine, so as read out the maximum echowaveform ve(t) from the waveform memory area of RAM 10 for Fouriertransformation and determine the maximum echo spectrum Ve(ω). Thecomplex reflection coefficient calculating routine is then executed soas to calculate the ultrasonic complex reflection coefficient R(ω) atthe interface between the patient's soft tissue Ma and bone at anangular frequency ω on the basis of the maximum echo spectrum Ve(ω) thuscalculated. The ultrasonic complex reflection coefficient R(ω) in thisexample is derived by means of Formula (29), in the same manner as inthe eighth embodiment, using the maximum echo spectrum Ve(ω) and echoarrival time Ta during the maximum level for the patient's bone, as wellas the maximum echo spectrum Vu(ω), echo arrival time Tu during themaximum level, and the ultrasonic complex reflection coefficient Ru(ω)for pseudo-cortical bone.

The maximum echo spectrum Vu(ω) and the echo arrival time Tu during themaximum level for pseudo-cortical bone were determined forpseudo-cortical bone of known ultrasonic complex reflection coefficientRu(ω) by roughly the same procedure as that when the maximum echowaveform and echo arrival time during the maximum level were determinedfor pseudo-cortical bone in the eighth embodiment, and were stored alongwith the known ultrasonic complex reflection coefficient Ru(ω) in ROM 9.In this example, however, the maximum echo spectrum Vu(ω) and echoarrival time Tu during the maximum level for pseudo-cortical bone wereobtained by first immersing pseudo-cancellous bone consisting of asubstance having acoustic properties similar to those of cancellous boneMc in a water tank filled with water or the like, placingpseudo-cortical bone of a predetermined thickness on thepseudo-cancellous bone, then arranging the transducer 1 at a distancecorresponding to a standard thickness of soft tissue Ma with respect tothe pseudo-cortical bone, emitting an ultrasonic pulse Ai at thepseudo-cortical bone, and executing the Fourier transform process or thelike described above on the echo data thus obtained. The CPU 11 thenmoves to the complex acoustic impedance calculating routine, and theultrasonic complex reflection coefficient R(ω) thus calculated issubstituted into Formula (27) to determine the complex acousticimpedance Z(ω) for the patient's bone (step SR202). The CPU 11 thendetermines the complex acoustic impedance Zc(ω) for the patient'scancellous bone and the area density σ of the cortical bone Mb from theresulting complex acoustic impedance Z(ω) for bone and Formula (35)(stepSR203), and displays them on the screen of the display 13 (step SR204).

The structure of the ninth embodiment allows data such as the areadensity σ to be obtained even when the cortical bone Mb is thinner thanthe ultrasonic wavelength. In this case, the bone density ρ of thecortical bone Mb can also be learned when the thickness L of thepatient's cortical bone Mb is known. The complex acoustic impedance Zcfor cancellous bone Mc can also be learned.

Embodiment 10

FIG. 15 is a flow chart of the operation and processing procedures ofthe apparatus for diagnosing osteoporosis in a tenth embodiment of thepresent invention.

The hardware in the tenth embodiment has roughly the same structure asthat in the eighth embodiment, so the structure in this example will bedescribed with reference to FIG. 11. In the structure of the apparatusfor diagnosing osteoporosis in this example, the attenuation A(T) duringthe reciprocal movement of the ultrasonic wave through soft tissue Ma istaken into account, allowing the acoustic impedance Zb for cortical boneMb to be measured with even greater accuracy. The apparatus main unit 2ain this example has a timing circuit 14 for measuring the echo arrivaltime T from after the emission of the ultrasonic impulse Ai from thetransducer surface of the transducer 1 until the echo Ae returns to thetransducer surface. The processing program in this example includes aprocedure in which the ultrasonic reflection coefficient R for corticalbone Mb relative to the soft tissue Ma of the patient is calculated onthe basis of the maximum echo level and the echo arrival time T at thistime.

The operation of this example (primarily the processing of the CPU 11during the diagnosis of osteoporosis) is described below with referenceto FIG. 15.

After the CPU 11 has sent a 1 pulse generating command to the pulsegenerator 4 (step ST12), it issues a sampling start command (step SP13)to the A/D convertor 8 upon measuring the time in which the transmissionresonance An₁ is received by the ultrasonic oscillator 1a of thetransducer 1, the echo An₂ from the skin is then received, and the echoAe from the cortical bone Mb returns to the transducer surface of theoscillator 1a of the transducer 1. In step ST14, the CPU 11 then readsthe echo waveform (echo signal) from the A/D convertor 8a, reads theecho arrival time T from the timing circuit 14, and stores the currentecho waveform (current echo signal) and echo arrival time T thus read inthe echo data memory area of RAM 10. After the conclusion of themeasurement (steps ST19 and ST20), the CPU 11 first moves to theultrasonic attenuation calculating routine to read RAM 10, andsubstitutes the echo arrival time Tsec into Formula (36) to calculatethe ultrasonic attenuation A(T) in the patient's soft tissue Ma (stepST201). ##EQU8##

Here, the attenuation A(T) means the level of attenuation during thereciprocal movement of the ultrasonic waves in soft tissue Ma, that is,the attenuation when the ultrasonic waves are propagated from thesurface X of the skin to the surface Y of the of the cortical bone Mband are reflected at the surface Y of the cortical bone Mb back again tothe surface X of the skin (the lower the A(T), the greater theattenuation). The attenuation A(T) is a function of the echo arrivaltime T, the relation of which is determined by experiment or simulation.

Ultrasonic waves undergo attenuation in the soft tissue Ma because,first, the ultrasonic waves used in this example are not completelyflat, but also contain multiple spherical wave components, resulting inthe scattering of acoustic energy (ultrasonic scattering), and second,because acoustic energy is converted to thermal energy (ultrasonicabsorption) by friction with the soft tissue Ma. The extent ofattenuation caused by ultrasonic scattering can be determined bymeasurement or experiment from the aperture of the transducer 1,ultrasonic frequency, acoustic velocity of soft tissue Ma, and the like.

The extent of attenuation caused by ultrasonic absorption is lower whenthe ultrasonic frequency is lower, and an absorption constant typical ofsoft tissue Ma (ultrasonic attenuation rate per unit length) can be usedeven when the frequency is not sufficiently low. Formula (36) giving theultrasonic attenuation A(T) is an empirical formula that is obtainedwhen the central ultrasonic frequency used is set at 2.5 MHz, and theaperture of the transducer 1 is set at 15 mm.

The CPU 11 then reads the maximum echo level Ve from the echo datamemory area of RAM 10 and substitutes it along with the calculatedattenuation A(T) into Formula (37) to calculate the ultrasonicreflection coefficient R at the interface between soft tissue Ma andcortical bone Mb when the ultrasonic waves land perpendicular on thecortical bone Mb from the soft tissue Ma (step ST21).

    R=Ve/P·Q·B·Vi·A(T)     (37)

Here, P, Q, B, and Vi mean the same as in Formula (10). Formula (37) isderived in the following manner. First, when an electrical signal ofamplitude Vi is applied from the pulse generator 4 to the transducer 1,an ultrasonic impulse Ai of a sound pressure PVi is introduced from thetransducer surface of the transducer 1 into the soft tissue Ma. As theultrasonic impulse Ai thus introduced is attenuated during itspropagation in the soft tissue Ma (assuming it lands perpendicular tothe surface Y of the cortical bone Mb), it is reflected perpendicularlyat the surface Y of the cortical bone Mb, resulting in echo Ae, andreturns perpendicular to the transducer 1. The sound pressure P(e) ofthe echo Ae returning to the transducer surface of the transducer 1 isthus given by Formula (38), taking into account the attenuation A(T)during the reciprocal movement of the ultrasonic waves in soft tissue Madetermined from Formula (36).

    P(e)=P·Vi·R·A(T)                (38)

When an echo Ae having a sound pressure P(e) is received at thetransducer surface of the transducer 1, the transducer 1 outputs areception signal having an amplitude Q·P(e), and this reception signalis amplified at an amplitude B by the amplifier 6 (and waveform shaper7). Following digital conversion by the A/D convertor 8a, the signal istaken in by the CPU 11 and detected in the form of the maximum echolevel Ve (=B·Q·P(e)). The maximum echo level Ve is thus given by Formula(39).

    Ve=P·Vi·R·A(T)·B·Q(39)

Formula (37) is obtained when Formula (39) is solved for the ultrasonicreflection coefficient R. To return to the description of the flow chartin FIG. 15, the CPU 11 calculates the ultrasonic reflection coefficientR at the interface between soft tissue Ma and cortical bone Mb usingFormula (37) (step ST21), and displays the calculated results on thescreen of the display 13 (step ST22). The CPU 11 calculates the acousticimpedance Zb for the patient's cortical bone Mb using Formula (5) (stepST23), and displays the calculated results on the screen of the display13 (step ST24).

Subsequently, the bone density of the patient's cortical bone Mb(density of cortical bone) ρ is calculated (step ST25) on the basis ofthe calculated value of the acoustic impedance Zb by the same means asin the first through seventh embodiments described above, and thecalculated results are displayed on the screen of the display 13 (stepST26).

In the structure described above, the attenuation A(T) during thereciprocal movement of the ultrasonic waves in soft tissue Ma is takeninto consideration in addition to the effects of the first embodimentdescribed above, allowing the acoustic impedance Zb of cortical bone Mband the bone density ρ of cortical bone Mb to be measured with evengreater accuracy.

Embodiments of the present invention were described in detail above withreference to figures, but the specific structure is not limited to theseembodiments, and the present invention includes modifications in designand the like which are within the essential scope of the presentinvention. For example, the bone serving as the measuring site is notlimited to cortical bone such as the tibia, the top of the patella, orthe heel, as long as it can be considered flat. The ultrasonicoscillator constituting the transducer is not limited to a thicknessoscillation type and may be a flexural oscillation type.

Since the acoustic impedance of soft tissue Ma is close to the acousticimpedance of 1.5×10⁶ kg/m² sec for water, the acoustic impedance forwater may be used instead of that for soft tissue Ma to calculate theultrasonic reflection coefficient using Formula (31). The variousprocessing programs of the CPU 11 may be stored in an external memorydevice such as a hard disk as needed instead of being stored in ROM 9.Part or all of the structural components of the apparatus for diagnosingosteoporosis in the present invention may be hardware structures andsoftware structures.

The method for calculating the ultrasonic reflection coefficient R isnot limited to the methods described in the embodiments above. Forexample, when one end surface of the transducer 1 is a free end andechoes are measured from one end surface, the ultrasonic waves arecompletely reflected at one end surface, so the reflection level at thistime is equivalent to the incident wave level. As such, the ultrasonicreflection coefficient R can be determined as the ratio between theincident wave level and the echo level from the cortical bone Mb.

In the first embodiment described above, the regression coefficient aused in the recurrence formula for calculating bone density was1.80×10⁻⁴, but, as is apparent in the third embodiment, the regressioncoefficient α should range from 1.27×10⁻⁴ to 2.34×10⁻⁴. Similarly, thesection β is constant at 766, but may range from 646 to 887. In thefourth embodiment described above, the regression coefficient A used inthe recurrence formula for calculating bone density was 0.342, but, asis apparent in the fifth embodiment, the regression coefficient A shouldrange from 0.239 to 0.445. Similarly, the constant B was constant at10⁰.894, but may range from 10⁰.239 to 10¹.55. In the sixth embodimentdescribed above, the regression coefficient α' used in the recurrenceformula for calculating bone density was 843, but, as is apparent in theseventh embodiment, it may range form 588 to 1100. Similarly, thesection β' was constant at 1000, but may range from 953 to 1060.

In the fourth embodiment described above, a nonlinear recurrence formula(Formula (15)) for bone density ρ relative to acoustic impedance Zb wasused, but as indicated in Formula (40), a nonlinear recurrence formulafor the density of cortical bone relative to ultrasonic reflectioncoefficient can similarly be used.

    ρ=B'R.sup.A '                                          (40)

ρ: cortical bone density kg/m³ !

R: ultrasonic reflection coefficient at interface between soft tissueand cortical bone of patient

A': regression index

B': constant sec/m!

INDUSTRIAL APPLICABILITY

The ultrasonic reflection type of apparatus and method for diagnosingosteoporosis in the present invention are suitable for use in hospitals,sports facilities, health care facilities, and the like, but since theapparatus is compact and light-weight, is easy to operate, and is freeof the danger of radiation exposure, it is particularly desirable foruse as a household health management instrument for the elderly.

What is claimed is:
 1. An ultrasonic reflection type of apparatus fordiagnosing osteoporosis having an ultrasonic transducer for transmittingand receiving ultrasonic pulses, wherein the ultrasonic pulses arerepeatedly radiated toward cortical bone in a subject, the echoesreflected on the surface of the cortical bone at that time are received,the density of the subject's cortical bone is calculated based on theresulting echo data, and osteoporosis is diagnosed based on corticalbone density thus calculated, said apparatus for diagnosing osteoporosiscomprising:echo level detecting means for detecting the echo level ofthe echoes reflected on the surface of the cortical bone when theultrasonic pulses are radiated; maximum echo level extracting means forextracting the maximum echo level from among the echo levels thusdetected; reflection coefficient calculating means for calculating theultrasonic reflection coefficient at the interface between the softtissue and cortical bone of the subject based on the extracted maximumecho level; and bone density calculating means for calculating thedensity of the subject's cortical bone using a predetermined recurrenceformula for said cortical bone density relative to said ultrasonicreflection coefficient.
 2. An ultrasonic reflection type of apparatusfor diagnosing osteoporosis having an ultrasonic transducer fortransmitting and receiving ultrasonic pulses, wherein the ultrasonicpulses are repeatedly radiated toward cortical bone in a subject, theechoes reflected on the surface of the cortical bone at that time arereceived, the density of the subject's cortical bone is calculated basedon the resulting echo data, and osteoporosis is diagnosed based oncortical bone density thus calculated, said apparatus for diagnosingosteoporosis comprising:echo level detecting means for detecting theecho level of the echoes reflected on the surface of the cortical bonewhen the ultrasonic pulses are radiated; maximum echo level extractingmeans for extracting the maximum echo level from among said echo levels;acoustic impedance calculating means for calculating the acousticimpedance of the subject's cortical bone based on the extracted maximumecho level; and bone density calculating means for calculating thedensity of the subject's cortical bone using a predetermined recurrenceformula for said cortical bone density relative to said acousticimpedance.
 3. An apparatus for diagnosing osteoporosis as defined inclaim 2, wherein said acoustic impedance calculating means calculatesthe ultrasonic reflection coefficient of the cortical bone relative tothe soft tissue of the subject based on the maximum echo level extractedby the maximum echo level extracting means, and then calculates saidacoustic impedance of the subject's cortical bone based on ultrasonicreflection coefficient thus calculated.
 4. An ultrasonic reflection typeof apparatus for diagnosing osteoporosis having an ultrasonic transducerfor transmitting and receiving ultrasonic pulses, wherein the ultrasonicpulses are repeatedly radiated toward cortical bone in a subject, theechoes reflected on the surface of the cortical bone at that time arereceived, the density of the subject's cortical bone is calculated basedon the resulting echo data, and osteoporosis is diagnosed based oncortical bone density thus calculated, said apparatus for diagnosingosteoporosis comprising:echo level detecting means for detecting theecho level of the echoes reflected on the surface of the cortical bonewhen the ultrasonic pulses are radiated; a maximum echo level extractingprogram containing the processing procedure for extracting the maximumecho level from among the echo levels thus detected; a reflectioncoefficient calculating program containing the processing procedure forcalculating the ultrasonic reflection coefficient at the interfacebetween the soft tissue and cortical bone of the subject based onmaximum echo level that has been extracted; a bone density calculatingprogram containing the processing procedure for calculating the densityof the subject's cortical bone using a predetermined recurrence formulafor said cortical bone density relative to said ultrasonic reflectioncoefficient; a first memory for storing various processing programs,including the maximum echo level extracting program, reflectioncoefficient calculating program, and bone density calculating program; asecond memory for temporarily storing data, including the echo levelsthus detected and maximum echo levels that have been extracted; and acentral processing unit for calculating the density of the subjects'cortical bone by using said second memory to execute the variousprograms stored in said first memory.
 5. An ultrasonic reflection typeof apparatus for diagnosing osteoporosis having an ultrasonic transducerfor transmitting and receiving ultrasonic pulses, wherein the ultrasonicpulses are repeatedly radiated toward cortical bone in a subject, theechoes reflected on the surface of the cortical bone at that time arereceived, the density of the subject's cortical bone is calculated basedon the resulting echo data, and osteoporosis is diagnosed based oncortical bone density thus calculated, said apparatus for diagnosingosteoporosis comprising:echo level detecting means for detecting theecho level of the echoes reflected on the surface of the cortical bonewhen the ultrasonic pulses are radiated; a maximum echo level extractingprogram containing the processing procedure for extracting the maximumecho level from among the echo levels thus detected; an acousticimpedance calculating program containing the processing procedure forcalculating the acoustic impedance of the subject's cortical bone basedon maximum echo level that has been extracted; a bone densitycalculating program containing the processing procedure for calculatingthe density of the subject's cortical bone using a predeterminedrecurrence formula for said cortical bone density relative to saidacoustic impedance; a first memory for storing various processingprograms, including the maximum echo level extracting program,reflection coefficient calculating program, acoustic impedancecalculating program, and bone density calculating program; a secondmemory for temporarily storing data, including the detected echo levelsand extracted maximum echo levels; and a central processing unit forcalculating the density of the subjects' cortical bone by using saidsecond memory to execute the various programs stored in said firstmemory.
 6. An apparatus for diagnosing osteoporosis as defined in claim5, wherein said acoustic impedance calculating program contains theprocessing procedure for calculating said ultrasonic reflectioncoefficient of the cortical bone relative to the soft tissue of thesubject based on said maximum echo level extracted by said maximum echolevel extracting means, and the processing procedure for calculatingsaid acoustic impedance of the subject's cortical bone based onultrasonic reflection coefficient thus calculated.
 7. An apparatus fordiagnosing osteoporosis as defined in claim 1 or claim 4, wherein saidrecurrence formula for said cortical bone density relative to saidultrasonic reflection coefficient is given in the form of the followingformula.

    ρ=α'R+β'

ρ: density of cortical bone kg/m³ ! R: ultrasonic reflection coefficientat interface between soft tissue and cortical bone of subject α':regression coefficient kg/m³ ! β': section kg/m³ !
 8. An apparatus fordiagnosing osteoporosis as defined in claim 7, wherein aid regressioncoefficient α' is established within the range of 588 to
 1100. 9. Anapparatus for diagnosing osteoporosis as defined in claim 7, whereinsaid section β' is established within the range of 953 to
 1060. 10. Anapparatus for diagnosing osteoporosis as defined in claim 1 or claim 4,wherein said recurrence formula for said cortical bone density relativeto said ultrasonic reflection coefficient is given in the form of thefollowing formula.

    ρ=B'R.sup.A '

ρ: density of cortical bone kg/m³ ! R: ultrasonic reflection coefficientat interface between soft tissue and cortical bone of subject A':regression coefficient B': constant sec/m!
 11. An apparatus fordiagnosing osteoporosis as defined in claim 3 or claim 6, wherein saidacoustic impedance of the subject's cortical bone is given by thefollowing formula,

    Zb=Za(R+1)/(1-R)

Zb: acoustic impedance of cortical bone in subject Za: acousticimpedance of soft tissue or acoustic impedance of water R: ultrasonicreflection coefficient at interface between soft tissue and corticalbone of subject
 12. An apparatus for diagnosing osteoporosis as definedin claim 2 or claim 5, wherein said recurrence formula for said corticalbone density relative to said acoustic impedance is given by thefollowing formula.

    ρ=αZb+β

ρ: density of cortical bone kg/m³ ! Zb: acoustic impedance of corticalbone in subject kg/m² sec! α: regression coefficient sec/m! β: sectionkg/m³ !
 13. An apparatus for diagnosing osteoporosis as defined in claim12, wherein said regression coefficient α is established within therange of 1.27×10⁻⁴ to 2.34×10⁻⁴.
 14. An apparatus for diagnosingosteoporosis as defined in claim 12, wherein said section β isestablished within the range of 646 to
 887. 15. An apparatus fordiagnosing osteoporosis as defined in claim 2 or claim 5, wherein saidrecurrence formula for cortical bone density relative to acousticimpedance is given by the following formula.

    ρ=BZb.sup.A

ρ: density of cortical bone kg/m³ ! Zb: acoustic impedance of corticalbone in subject kg/m² sec! A: regression coefficient B: constant sec/m!16. An apparatus for diagnosing osteoporosis as defined in claim 15,wherein said regression coefficient A is established within the range of0.239 to 0.445.
 17. An apparatus for diagnosing osteoporosis as definedin claim 15, wherein said constant B is established within the range of10⁰.239 to 10¹.55.
 18. An ultrasonic reflection type of apparatus fordiagnosing osteoporosis having an ultrasonic transducer for transmittingand receiving ultrasonic pulses, wherein the ultrasonic pulses arerepeatedly radiated toward cortical bone in a subject, the echoesreflected on the surface of the cortical bone at that time are received,complex acoustic characteristics data of the subject's cortical bone arecalculated based on the resulting echo data, and osteoporosis isdiagnosed based on complex acoustic characteristics data thuscalculated, said apparatus for diagnosing osteoporosis comprising:echowaveform detecting means for detecting the reception waveform of theechoes reflected on the surface of the cortical bone when the ultrasonicpulses are radiated; maximum echo waveform extracting means forextracting the maximum echo reception waveform by comparing theplurality of the echo reception waveforms thus detected; Fouriertransform treatment means for finding the maximum echo spectrum by theFourier transform treatment of the maximum echo reception waveform; andcomplex reflection coefficient calculating means for calculating theultrasonic complex reflection coefficient of cortical bone relative tothe soft tissue of the subject based on the maximum echo spectrum thusdetermined.
 19. An apparatus for diagnosing osteoporosis as defined inclaim 18, further comprising a diagnostic means for diagnosingosteoporosis based on the amplitude data and phase data obtained fromultrasonic complex reflection coefficient thus calculated.
 20. Anultrasonic reflection type of apparatus for diagnosing osteoporosishaving an ultrasonic transducer for transmitting and receivingultrasonic pulses, wherein the ultrasonic pulses are repeatedly radiatedtoward cortical bone in a subject, the echoes reflected on the surfaceof the cortical bone at that time are received, complex acousticcharacteristics data of the subject's cortical bone are calculated basedon the resulting echo data, and osteoporosis is diagnosed based oncomplex acoustic characteristics data thus calculated, said apparatusfor diagnosing osteoporosis comprising:echo waveform detecting means fordetecting the reception waveform of the echoes reflected on the surfaceof the cortical bone when the ultrasonic pulses are radiated; maximumecho waveform extracting means for extracting the maximum echo receptionwaveform by comparing the plurality of the echo reception waveforms thusdetected; Fourier transform treatment means for finding the maximum echospectrum by the Fourier transform treatment of the maximum echoreception waveform; and complex acoustic impedance calculating means forcalculating the complex acoustic impedance of the subject's corticalbone based on the maximum echo spectrum thus determined.
 21. Anapparatus for diagnosing osteoporosis as defined in claim 20, whereinsaid complex acoustic impedance calculating means calculates theultrasonic complex reflection coefficient of the cortical bone relativeto the soft tissue of the subject based on the maximum echo spectrumdetermined by the Fourier transform treatment means, and then calculatesthe complex acoustic impedance of the subject's cortical bone based onultrasonic complex reflection coefficient thus calculated.
 22. Anapparatus for diagnosing osteoporosis as defined in claim 21, whereinsaid acoustic impedance of the subject's cortical bone is given by thefollowing formula,

    Zb(ω)=Za(ω)(R(ω)+1)/(1-R(ω))

Zb(ω): acoustic impedance of cortical bone in Subject during angularfrequency ω Za(ω): acoustic impedance of soft tissue or acousticimpedance of water during angular frequency ω R(ω): ultrasonic complexreflection coefficient at interface between soft tissue and corticalbone of subject
 23. An apparatus for diagnosing osteoporosis as definedin claim 20, 21, or 22, further comprising diagnostic means fordiagnosing osteoporosis based on the amplitude data and phase dataobtained from complex acoustic impedance thus calculated.
 24. Anultrasonic reflection type of apparatus for diagnosing osteoporosishaving an ultrasonic transducer for transmitting and receivingultrasonic pulses, wherein the ultrasonic pulses are repeatedly radiatedtoward cortical bone in a subject, the echoes reflected on the surfaceof the cortical bone at that time are received, complex acousticcharacteristics data of the subject's cortical bone are calculated basedon the resulting echo data, and osteoporosis is diagnosed based oncomplex acoustic characteristics data thus calculated, said apparatusfor diagnosing osteoporosis comprising:an echo waveform detectingprogram containing a processing procedure for detecting the receptionwaveform of the echoes reflected on the surface of the cortical bonewhen the ultrasonic pulses are radiated; a maximum echo waveformextracting program containing a processing procedure for extracting themaximum echo reception waveform by comparing the plurality of the echoreception waveforms thus detected; a Fourier transform treatment programcontaining a processing procedure for finding the maximum echo spectrumby the Fourier transform treatment of the maximum echo receptionwaveform; a complex reflection coefficient calculating programcontaining a processing procedure for calculating the ultrasonic complexreflection coefficient of cortical bone in the subject based on themaximum echo spectrum thus determined; a first memory for storingvarious processing programs, including the echo waveform detectingprogram, maximum echo waveform extracting program, Fourier transformtreatment program, and complex reflection coefficient calculatingprogram; a second memory for temporarily storing data, including thedetected echo reception waveform, and the extracted maximum echoreception waveform and spectrum; and a central processing unit forcalculating the ultrasonic complex reflection coefficient of thesubjects' cortical bone by using said second memory to execute thevarious programs stored in said first memory.
 25. An ultrasonicreflection type of apparatus for diagnosing osteoporosis having anultrasonic transducer for transmitting and receiving ultrasonic pulses,wherein the ultrasonic pulses are repeatedly radiated toward corticalbone in a subject, the echoes reflected on the surface of the corticalbone at that time are received, complex acoustic characteristics data ofthe subject's cortical bone are calculated based on the resulting echodata, and osteoporosis is diagnosed based on complex acousticcharacteristics data thus calculated, said apparatus for diagnosingosteoporosis comprising:an echo waveform detecting program containing aprocessing procedure for detecting the reception waveform of the echoesreflected on the surface of the cortical bone when the ultrasonic pulsesare radiated; a maximum echo waveform extracting program containing aprocessing procedure for extracting the maximum echo reception waveformby comparing the plurality of the echo reception thus detected; aFourier transform treatment program containing a processing procedurefor finding the maximum echo spectrum by the Fourier transform treatmentof the maximum echo reception waveform; a complex acoustic impedancecalculating program containing a processing procedure for calculatingthe complex acoustic impedance of cortical bone in the subject based onthe maximum echo spectrum thus determined; a first memory for storingvarious processing programs, including the echo waveform detectingprogram, maximum echo waveform extracting program, Fourier transformtreatment program, and complex acoustic impedance calculating program; asecond memory for temporarily storing data, including the detected echoreception waveform, and the extracted maximum echo reception waveformand spectrum; and a central processing unit for calculating the complexacoustic impedance of the subjects' cortical bone by using said secondmemory to execute the various programs stored in said first memory. 26.An apparatus for diagnosing osteoporosis as defined in claim 25, whereinsaid complex acoustic impedance calculating program contains theprocessing procedure for calculating the ultrasonic complex reflectioncoefficient of the cortical bone in the subject based on the maximumecho spectrum which has been determined, and the processing procedurefor calculating the acoustic impedance of the subject's cortical bonebased on ultrasonic reflection coefficient thus calculated.
 27. A methodfor diagnosing osteoporosis comprising the steps of:setting anultrasonic transducer on a predetermined area on the surface of asubject's skin; repeatedly radiating ultrasonic pulses toward corticalbone below the skin; receiving the echoes reflected on the surface ofthe cortical bone at that time, so as to detect the echo level;extracting the maximum echo level from the echo levels thus detected;calculating the ultrasonic reflection coefficient at the interfacebetween the soft tissue and the cortical bone of the subject based onmaximum echo level thus calculated; and calculating the density of thesubject's cortical bone using a predetermined recurrence formula for thecortical bone density relative to the ultrasonic reflection coefficient.28. A method for diagnosing osteoporosis comprising the steps of:settingan ultrasonic transducer on a predetermined area on the surface of asubject's skin; repeatedly radiating ultrasonic pulses toward corticalbone below the skin; receiving the echoes reflected on the surface ofthe cortical bone at that time, so as to detect the echo level;extracting the maximum echo level from the echo levels thus detected;calculating the acoustic impedance of the cortical bone of the subjectbased on the maximum echo level that has been extracted; and calculatingthe density of the subject's cortical bone using a predeterminedrecurrence formula for said cortical bone density relative to saidacoustic impedance.
 29. A method for diagnosing osteoporosis, comprisingthe steps of:setting an ultrasonic transducer on a predetermined area onthe surface of a subject's skin; repeatedly radiating ultrasonic pulsestoward cortical bone below the skin; reflecting at the transducersurface the echoes reflected on the surface of the cortical bone at thattime, so as to detect the echo level; extracting the maximum echo levelfrom the echo levels thus detected; calculating the ultrasonicreflection coefficient at the interface between the soft tissue and thecortical bone of the subject, based on the maximum echo level that hasbeen extracted; calculating the acoustic impedance of the cortical boneof the subject based on ultrasonic reflection coefficient thuscalculated; and calculating the density of the subject's cortical boneusing a predetermined recurrence formula for said cortical bone densityrelative to said acoustic impedance.
 30. A method for diagnosingosteoporosis as defined in claim 27, wherein said recurrence formula forsaid cortical bone density relative to said ultrasonic reflectioncoefficient is given in the form of the following formula.

    ρ=α'R+β'

ρ: density of cortical bone kg/m³ ! R: ultrasonic reflection coefficientat interface between soft tissue and cortical bone of subject α':regression coefficient kg/m³ ! β': section kg/m³ !
 31. A method fordiagnosing osteoporosis as defined in claim 30, wherein said regressioncoefficient α' is established within the range of 588 to
 1100. 32. Amethod for diagnosing osteoporosis as defined in claim 30, wherein saidsection β' is established within the range of 953 to
 1060. 33. A methodfor diagnosing osteoporosis as defined in claim 28 or claim 29, whereinsaid recurrence formula for said cortical bone density relative to saidultrasonic reflection coefficient is given in the form of the followingformula.

    ρ=B'R.sup.A '

ρ: density of cortical bone kg/m³ ! R: ultrasonic reflection coefficientat interface between soft tissue and cortical bone of subject A':regression coefficient B': constant sec/m!
 34. A method for diagnosingosteoporosis as defined in claim 29, wherein said acoustic impedance ofthe subject's cortical bone is given by the following formula,

    Zb=Za(R+1)/(1-R)

Zb: acoustic impedance of cortical bone in subject Za: acousticimpedance of soft tissue or acoustic impedance of water R: ultrasonicreflection coefficient at interface between soft tissue and corticalbone of subject
 35. A method for diagnosing osteoporosis as defined inclaim 28 or claim 29, wherein said recurrence formula for cortical bonedensity relative to acoustic impedance is given by the followingformula.

    ρ=αZb+β

ρ: density of cortical bone kg/m³ ! Zb: acoustic impedance of corticalbone in subject kg/m² sec! α: regression coefficient sec/m! β: sectionkg/m³ !
 36. A method for diagnosing osteoporosis as defined in claim 35,wherein said regression coefficient α is established within the range of1.27×10⁻⁴ to 2.34×10⁻⁴.
 37. A method for diagnosing osteoporosis asdefined in claim 35, wherein said section β is established within therange of 646 to
 887. 38. A method for diagnosing osteoporosis as definedin claim 28 or claim 29, wherein said recurrence formula for corticalbone density relative to acoustic impedance is given by the followingformula.

    ρ=BZb.sup.A

ρ: density of cortical bone kg/m³ ! Zb: acoustic impedance of corticalbone in subject kg/m² sec! A: regression coefficient B: constant sec/m!39. A method for diagnosing osteoporosis as defined in claim 38, whereinsaid regression coefficient A is established within the range of 0.239to 0.445.
 40. A method for diagnosing osteoporosis as defined in claim38, wherein said constant B is established within the range of 10⁰.239to 10¹.55.
 41. A method for diagnosing osteoporosis, comprising thesteps of:setting an ultrasonic transducer a predetermined area on thesurface of a subject's skin; repeatedly radiating ultrasonic pulsestoward cortical bone below the skin; receiving the reception waveform ofthe echoes reflected on the surface of the cortical bone at that time,so as to detect the echo reception waveform; extracting the detectedmaximum echo from the echo reception waveform; determining the maximumecho spectrum by the Fourier transform treatment of the maximum echoreception waveform; calculating the ultrasonic complex reflectioncoefficient of the cortical bone relative to the soft tissue of thesubject based on the maximum echo spectrum that has been determined; anddiagnosing osteoporosis based on the amplitude data and phase dataobtained from ultrasonic complex reflection coefficient thus calculated.42. A method for diagnosing osteoporosis, comprising the stepsof:setting an ultrasonic transducer on a predetermined area on thesurface of a subject's skin; repeatedly radiating ultrasonic pulsestoward cortical bone below the skin; receiving the reception waveform ofthe echoes reflected on the surface of the cortical bone at that time,so as to detect the echo reception waveform; extracting the maximum echofrom the detected echo reception waveform; determining the maximum echospectrum by the Fourier transform treatment of the maximum echoreception waveform; calculating the complex acoustic impedance of thecortical bone of the subject based on the maximum echo spectrum that hasbeen determined; and diagnosing osteoporosis based on the amplitude dataand phase data obtained from complex acoustic impedance thus calculated.43. A method for diagnosing osteoporosis, comprising the stepsof:setting an ultrasonic transducer on a predetermined area on thesurface of a subject's skin; repeatedly radiating ultrasonic pulsestoward cortical bone below the skin; receiving the reception waveform ofthe echoes reflected on the surface of the cortical bone at that time,so as to detect the echo reception waveform; extracting the maximum echofrom the echo reception waveform thus detected; determining the maximumecho spectrum by the Fourier transform treatment of the maximum echoreception waveform; calculating the ultrasonic complex reflectioncoefficient of the cortical bone relative to the soft tissue of thesubject based on the maximum echo spectrum that has been determined;calculating the complex acoustic impedance of the cortical bone of thesubject based on ultrasonic complex reflection coefficient thuscalculated; and diagnosing osteoporosis based on the amplitude data andphase data obtained from complex acoustic impedance thus calculated. 44.A method for diagnosing osteoporosis as defined in claim 43, whereinsaid acoustic impedance of the subject's cortical bone is given by thefollowing formula.

    Zb(ω)=Za(ω)(R(ω)+1)/(1-R(ω))

Zb(ω): acoustic impedance of cortical bone in Subject during angularfrequency ω Za(ω): acoustic impedance of soft tissue or Acousticimpedance of water during angular frequency ω R(ω): ultrasonic complexreflection coefficient at interface between soft tissue and corticalbone of subject.
 45. A method for diagnosing osteoporosis as defined inany one of claim 27 through claim 44, wherein the cortical bone which isthe subject of diagnosis is the cortical bone of the cranial bone,tibia, or scapula.